TASK VI: Schrödinger Equation
Anjar Sari (1017016300991)
Physic Education V
SCHRODINGER QUATION
Schrödinger's Cat: A cat, along with a flask containing a poison, is placed in a sealed box shielded against environmentally induced quantum decoherence. If an internal Geiger counter detects radiation, the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when we look in the box, we see the cat either alive or dead, not a mixture of alive and dead.
Schrödinger's cat is a thought experiment, often described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung — literally, entanglement.
1. SCHRODINGER’S EQUATION FOR THE HYDROGEN
Schrödinger’s equation for the electron in three dimension, which is what we must use for the hydrogen atom, is
The potential energy U here is the electric potential energy
2. SEPARATION OF VARIABLE
Hydrogen atom wave function
When we substitute for in Schrödinger equation for the hydrogen atom and divide the entire equation by , we fine that
3. THE THOUGHT EXPERIMENT
Schrödinger wrote:
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.
The above text is a translation of two paragraphs from a much larger original article that appeared in the German magazine Naturwissenschaften ("Natural Sciences") in 1935.
Schrödinger's famous thought experiment poses the question, when does a quantum system stop existing as a mixture of states and become one or the other? (More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The purpose of the thought experiment is to illustrate this apparent paradox. Our intuition says that no observer can be in a mixture of states; yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Albert Einstein, who was impressed by the ability of the thought experiment to highlight these issues. In a letter to Schrödinger dated 1950, he wrote:
You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gunpowder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.
Note that no charge of gunpowder is mentioned in Schrödinger's setup, which uses a Geiger counter as an amplifier and hydrocyanic poison instead of gunpowder. The gunpowder had been mentioned in Einstein's original suggestion to Schrödinger 15 years before, and apparently Einstein had carried it forward to the present discussion.
4. ENSEMBLE INTERPRETATION
The ensemble interpretation states that superpositions are nothing but subensembles of a larger statistical ensemble. That being the case, the state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger's Cat paradox a trivial nonissue.
This interpretation serves to discard the idea that a single physical system in quantum mechanics has a mathematical description that corresponds to it in any way; the problem should be renamed Schrödinger's cats.
5. Objective collapse theories
According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time, mass, temperature, irreversibility, etc.) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as "the cat observes itself", or "the environment observes the cat".
Objective collapse theories require a modification of standard quantum mechanics to allow superpositions to be destroyed by the process of time evolution.
6. PRACTICAL APPLICATIONS
The experiment is a purely theoretical one, and the machine proposed is not known to have been constructed. Analogous effects, however, have some practical use in quantum computing and quantum cryptography. It is possible to send light that is in a superposition of states down a fiber optic cable. Placing a wiretap in the middle of the cable that intercepts and retransmits the transmission will collapse the wave function (in the Copenhagen interpretation, "perform an observation") and cause the light to fall into one state or another. By performing statistical tests on the light received at the other end of the cable, one can tell whether it remains in the superposition of states or has already been observed and retransmitted. In principle, this allows the development of communication systems that cannot be tapped without the tap being noticed at the other end. This experiment can be argued to illustrate that "observation" in the Copenhagen interpretation has nothing to do with consciousness (unless some version of panpsychism is true), in that a perfectly unconscious wiretap will cause the statistics at the end of the wire to be different. Such a test would only work if the collapse occurs after (as opposed to before) observation; otherwise, it would appear collapsed whether it had been wiretapped or not.
Selasa, 08 Desember 2009
tugas Quantum
TUGAS V: Dark and Bright Effect
Anjar Sari (1017016300991)
Physic Education V
DARK AND BRINGHT
1. THE PARTICLE WAVE DUALITY
In former times scientists thought that light consists of waves and that electrons, neutrons and protons are particles. But Scientists have discovered that sometimes light has got a wave character and sometimes light has got a particle character but not only light also the other particles which I mentioned sometimes have got a wave character. There is an experiment which shows that light can have a particle character.
For this experiment we need a metal plate. When we irradiate this metal plate with light it can happen that some of the electrons of some atoms will leave their atomic shell. But when no electron leaves the atomic shell a classical physicist would say that the intensity is to low and what we need a stronger light source or that we must give the light nearer to the metal plate. But this would not help, because light consists of photons and when we have got a higher intensity there are more photons which bombard the electrons, but one electron can only absorb one photon. This means that the energy of the photon is responsible, weather an electron leaves his atomic shell or not.
The electrons are hooded by the positive charged atomic nucleus and so they need a certain energy to break out. So we need radiation with a shorter wavelength to give the electrons enough energy. If the wavelength is shorter the energy and the frequency are higher. Which wavelength do we need depends on the atoms. Simple light is to little so that we need ultraviolet light for example. All this is called photoelectric effect. The best possibility to make this experiment is with an electroscope. There is also an experiment which show us that electrons can have a wave character. It is the double gap experiment which I will describe later, because he is the most important experiment for quantum physics and the consequences of him might change your conception of the world.
2. HEISENBERG'S UNCERTAINTY RELATION
To measure the position and the speed of a certain particle we need light or another radiation. When we use radiation with a long wavelength the position is inexact, but the speed is quite exact. When we use radiation with a short wavelength the position is quite exact, but the speed is inexact. This means that when we want to measure one of these things exact, we cannot measure the other thing exact, too. Some things which are explained in nuclear physics with a simple pattern cannot be explained in quantum physics so easy, too.
We have this problem with the Bohr atom model. In real there are not any electrons which fly around the atomic nucleus, but you imagine that they are on certain energy levels. In this situation it is also impossible to say exact where an electron is. So here we find Heisenberg's uncertainty relation, too. But there are so called orbital where it is very probable that there is an electron, but it is never sure. In quantum physics we have got only probabilities.
3. NOTHING IS REAL
The experiment begins very simple. You need a light source, a wall with two holes and a screen. On side of the wall there is the light source and on the other side there is the screen. When light passes the wall we can see an interference sample on the screen. The maxima are not behind the holes on the screen, but there is one maximum between the two holes on the screen, otherwise it would not be an interference sample.
On the right and on the left of this maximum there are dark areas and then again bright areas, but these bright areas are not as bright as the maximum in the middle. Then we have got two dark areas again and so on. This result should not wonder us, because this are waves and because some waves have got a longer way from the light source to the screen than other waves some waves strengthen each other and other waves extinguish each other. When two wave combs clash then they strengthen each other and when a wave comb and a wave valley clash then they extinguish each other. When one hole is closed the maximum is behind the opened hole.
Now we will replace the light source through an electron source and we will make the experiment again. This time we get the same interference sample when both holes are opened. This proofs the wave character of the electrons. But it is important that light or electrons cannot be a wave and a particle at the same time. Now it becomes interesting, we do not let many electrons through the wall, but only one after the other. When one electron passes the wall it cannot handicap himself and because it can only go through one of the holes it would be logical that the maxima are behind the two holes. But when we wait until many electrons have passed the wall we saw an interference sample again. When we repeat this experiment and we close one hole the maximum is behind the open hole. It seams that electron knows weather both holes are opened or only one. When we try to measure through which hole an electron goes we get two maxima behind the two holes.
So it is wrong to say that the electron goes through one of these two holes, because we can say that it goes through both holes or we can also say that it goes through not hole, both answers are correct. The consequence is that nothing is real until an observer saw it. We do not know a reciprocal action between the electron, the observer and the instruments, but there must exist a reciprocal action. An electron has got many possibilities and because of our oberservation the electron must choose one of the possible ways. So when it goes through one of the holes it is logical that the maxima are behind the holes. It is called collapse of the wave function and every particle has got a probability wave. This means that never can be sure where a particle is, we can only say where the most probable place is.
A human being has got also a probability wave which we can find in the whole universe, but her strongest point is there where we are. But there is every time a very little probability that you can find yourself on Mars for example or somewhere else, but this probability is so little that you need not be afraid. When we know through measurements where this person is then his wave function collapses, because we know his exact position. As long as we observe something it is real and when we do not observe it is not real any longer. There is another illustration which is called Schrödinger’s cat. It is a thought experiment. We give a cat into a box with a radioactive material and a bottle of poison. Because we never know when an atom decays a radioactive material is very good for this experiment.
The probability is very important for quantum physics. The box must be closed. When an atom of the radioactive material decays the bottle will be broken and the cat will die. But as long as we do not look after the cat if she is alive or dead, then we can say that she is alive and dead or not alive and not dead, both answers are correct. But in this situation we could not never say that she is alive or dead. I hope that these both experiments could tell you something about nature. So when you believe all this, which is not total sure until today, your conception of the world has changed I think.
4. THE SPACE-TIME AND TIME TRAVELS
Quantum physics is full of other phenomena. A very interesting possibility are time travels, because we see time travels in many movies, but only little propels know, that there are physical theories which make time travels possible. All what we know, it is space and time, we call it space-time. We always talk about three dimensions and a fourth dimension which is the time. There are so called space-time-diagrams. On the y-axle we have got the time and on the x-axle, the horizontal axle, we have got the space. In a diagram like that we can draw lines. When we stand for example the line is parallel to the y-axle, because only the time smears. When we travel faster the line comes closer to the x-axle.
The line of an object which has got an infinite speed would be parallel to the x-axle. All known movements can be illustrated in these space-time-diagrams. These lines go from the bottom to the top, from bottom left to top right or from bottom right to top left. Lines which go from the top to the bottom, top right to bottom left or top left to bottom right would be movements back into the past. We cannot imagine movements like that, but for photons which fly with the speed of light it do not matter if they go into the past or into the future.
The consequence might be for example that something can be formed of nothing, because Einstein's formula (E=mc2) allows to transform matter into energy and energy into matter. An electron-positron-pair for example can be formed by a no existing photon, which collide to form this photon. This is possible, because photon do not know the different between past and future. When we will crook the space-time so strong that the time will be one of the space dimensions and this space dimension will be the time then time travels could be possible, because in the space dimensions we can go forward and backward. In real it is very difficult to crook the space-time so strong, because we need a very strong gravity field. The possibility of time travels is fascinating.
5. THE MANY WORLDS THEORY
There also exist another theory which is called many worlds theory. She describes the nature without saying that something can be unreal. This theory says that there are many realities. So we can say that the electron in the double gap experiment goes in one reality through one hole and in another reality through the other hole. So we split one reality into two different realities. It grows like a tree with all his branch’s. We can also say that in our world Schrödinger’s cat is dead or alive and another reality it is the opposite. When we will travel in the time scientists think that if somebody kills his father before he was born then he disappears. But when there are many realities it can be possible to kill his father in one reality and then the person would not disappear. It is not sure if this theory is correct.
6. THE UNIFIED FIELD THEORY
The unified field theory is for modern physics the most important problem. This theory says that after the Big Bang only one unified power has existed. This GUT-Power (Grand Unified Theory) was divided into four fundamental powers.
The four fundamental powers
power range strength appearance
strong power 10-15 m 1 between quarks
electromagnetic power infinite 10-2 between charged particles
weak power 10-15 m 10-13 between leptons (neutrinos, elecrons)
gravity infinite 10-38 between all particles
Today we try to bring the four powers together. It has been discovered that a symmetry has existed between the electromagnetic power and the weak power which has broken. It is important to know that the W+-, the W-- and the Z0-particles are the exchange particles of the weak power. In our universe there is the highs field, which unified with the field of the weak power. With high energy it is possible to destroy the hags field and the exchange particles of the weak power are then free, they behave like photons and do not differ from them. For this discovery S. Glasgow, S. Weinberg and A. Salam got the noble price. In an experiment in the CERN (Conseil Europ�enne pour la Recherche Nucl�aire), in the proton-antiproton-collider this particles were found and so the electrical weak power was proofed. Now physicists work to find a connection between the electroweak power and the strong power.
Anjar Sari (1017016300991)
Physic Education V
DARK AND BRINGHT
1. THE PARTICLE WAVE DUALITY
In former times scientists thought that light consists of waves and that electrons, neutrons and protons are particles. But Scientists have discovered that sometimes light has got a wave character and sometimes light has got a particle character but not only light also the other particles which I mentioned sometimes have got a wave character. There is an experiment which shows that light can have a particle character.
For this experiment we need a metal plate. When we irradiate this metal plate with light it can happen that some of the electrons of some atoms will leave their atomic shell. But when no electron leaves the atomic shell a classical physicist would say that the intensity is to low and what we need a stronger light source or that we must give the light nearer to the metal plate. But this would not help, because light consists of photons and when we have got a higher intensity there are more photons which bombard the electrons, but one electron can only absorb one photon. This means that the energy of the photon is responsible, weather an electron leaves his atomic shell or not.
The electrons are hooded by the positive charged atomic nucleus and so they need a certain energy to break out. So we need radiation with a shorter wavelength to give the electrons enough energy. If the wavelength is shorter the energy and the frequency are higher. Which wavelength do we need depends on the atoms. Simple light is to little so that we need ultraviolet light for example. All this is called photoelectric effect. The best possibility to make this experiment is with an electroscope. There is also an experiment which show us that electrons can have a wave character. It is the double gap experiment which I will describe later, because he is the most important experiment for quantum physics and the consequences of him might change your conception of the world.
2. HEISENBERG'S UNCERTAINTY RELATION
To measure the position and the speed of a certain particle we need light or another radiation. When we use radiation with a long wavelength the position is inexact, but the speed is quite exact. When we use radiation with a short wavelength the position is quite exact, but the speed is inexact. This means that when we want to measure one of these things exact, we cannot measure the other thing exact, too. Some things which are explained in nuclear physics with a simple pattern cannot be explained in quantum physics so easy, too.
We have this problem with the Bohr atom model. In real there are not any electrons which fly around the atomic nucleus, but you imagine that they are on certain energy levels. In this situation it is also impossible to say exact where an electron is. So here we find Heisenberg's uncertainty relation, too. But there are so called orbital where it is very probable that there is an electron, but it is never sure. In quantum physics we have got only probabilities.
3. NOTHING IS REAL
The experiment begins very simple. You need a light source, a wall with two holes and a screen. On side of the wall there is the light source and on the other side there is the screen. When light passes the wall we can see an interference sample on the screen. The maxima are not behind the holes on the screen, but there is one maximum between the two holes on the screen, otherwise it would not be an interference sample.
On the right and on the left of this maximum there are dark areas and then again bright areas, but these bright areas are not as bright as the maximum in the middle. Then we have got two dark areas again and so on. This result should not wonder us, because this are waves and because some waves have got a longer way from the light source to the screen than other waves some waves strengthen each other and other waves extinguish each other. When two wave combs clash then they strengthen each other and when a wave comb and a wave valley clash then they extinguish each other. When one hole is closed the maximum is behind the opened hole.
Now we will replace the light source through an electron source and we will make the experiment again. This time we get the same interference sample when both holes are opened. This proofs the wave character of the electrons. But it is important that light or electrons cannot be a wave and a particle at the same time. Now it becomes interesting, we do not let many electrons through the wall, but only one after the other. When one electron passes the wall it cannot handicap himself and because it can only go through one of the holes it would be logical that the maxima are behind the two holes. But when we wait until many electrons have passed the wall we saw an interference sample again. When we repeat this experiment and we close one hole the maximum is behind the open hole. It seams that electron knows weather both holes are opened or only one. When we try to measure through which hole an electron goes we get two maxima behind the two holes.
So it is wrong to say that the electron goes through one of these two holes, because we can say that it goes through both holes or we can also say that it goes through not hole, both answers are correct. The consequence is that nothing is real until an observer saw it. We do not know a reciprocal action between the electron, the observer and the instruments, but there must exist a reciprocal action. An electron has got many possibilities and because of our oberservation the electron must choose one of the possible ways. So when it goes through one of the holes it is logical that the maxima are behind the holes. It is called collapse of the wave function and every particle has got a probability wave. This means that never can be sure where a particle is, we can only say where the most probable place is.
A human being has got also a probability wave which we can find in the whole universe, but her strongest point is there where we are. But there is every time a very little probability that you can find yourself on Mars for example or somewhere else, but this probability is so little that you need not be afraid. When we know through measurements where this person is then his wave function collapses, because we know his exact position. As long as we observe something it is real and when we do not observe it is not real any longer. There is another illustration which is called Schrödinger’s cat. It is a thought experiment. We give a cat into a box with a radioactive material and a bottle of poison. Because we never know when an atom decays a radioactive material is very good for this experiment.
The probability is very important for quantum physics. The box must be closed. When an atom of the radioactive material decays the bottle will be broken and the cat will die. But as long as we do not look after the cat if she is alive or dead, then we can say that she is alive and dead or not alive and not dead, both answers are correct. But in this situation we could not never say that she is alive or dead. I hope that these both experiments could tell you something about nature. So when you believe all this, which is not total sure until today, your conception of the world has changed I think.
4. THE SPACE-TIME AND TIME TRAVELS
Quantum physics is full of other phenomena. A very interesting possibility are time travels, because we see time travels in many movies, but only little propels know, that there are physical theories which make time travels possible. All what we know, it is space and time, we call it space-time. We always talk about three dimensions and a fourth dimension which is the time. There are so called space-time-diagrams. On the y-axle we have got the time and on the x-axle, the horizontal axle, we have got the space. In a diagram like that we can draw lines. When we stand for example the line is parallel to the y-axle, because only the time smears. When we travel faster the line comes closer to the x-axle.
The line of an object which has got an infinite speed would be parallel to the x-axle. All known movements can be illustrated in these space-time-diagrams. These lines go from the bottom to the top, from bottom left to top right or from bottom right to top left. Lines which go from the top to the bottom, top right to bottom left or top left to bottom right would be movements back into the past. We cannot imagine movements like that, but for photons which fly with the speed of light it do not matter if they go into the past or into the future.
The consequence might be for example that something can be formed of nothing, because Einstein's formula (E=mc2) allows to transform matter into energy and energy into matter. An electron-positron-pair for example can be formed by a no existing photon, which collide to form this photon. This is possible, because photon do not know the different between past and future. When we will crook the space-time so strong that the time will be one of the space dimensions and this space dimension will be the time then time travels could be possible, because in the space dimensions we can go forward and backward. In real it is very difficult to crook the space-time so strong, because we need a very strong gravity field. The possibility of time travels is fascinating.
5. THE MANY WORLDS THEORY
There also exist another theory which is called many worlds theory. She describes the nature without saying that something can be unreal. This theory says that there are many realities. So we can say that the electron in the double gap experiment goes in one reality through one hole and in another reality through the other hole. So we split one reality into two different realities. It grows like a tree with all his branch’s. We can also say that in our world Schrödinger’s cat is dead or alive and another reality it is the opposite. When we will travel in the time scientists think that if somebody kills his father before he was born then he disappears. But when there are many realities it can be possible to kill his father in one reality and then the person would not disappear. It is not sure if this theory is correct.
6. THE UNIFIED FIELD THEORY
The unified field theory is for modern physics the most important problem. This theory says that after the Big Bang only one unified power has existed. This GUT-Power (Grand Unified Theory) was divided into four fundamental powers.
The four fundamental powers
power range strength appearance
strong power 10-15 m 1 between quarks
electromagnetic power infinite 10-2 between charged particles
weak power 10-15 m 10-13 between leptons (neutrinos, elecrons)
gravity infinite 10-38 between all particles
Today we try to bring the four powers together. It has been discovered that a symmetry has existed between the electromagnetic power and the weak power which has broken. It is important to know that the W+-, the W-- and the Z0-particles are the exchange particles of the weak power. In our universe there is the highs field, which unified with the field of the weak power. With high energy it is possible to destroy the hags field and the exchange particles of the weak power are then free, they behave like photons and do not differ from them. For this discovery S. Glasgow, S. Weinberg and A. Salam got the noble price. In an experiment in the CERN (Conseil Europ�enne pour la Recherche Nucl�aire), in the proton-antiproton-collider this particles were found and so the electrical weak power was proofed. Now physicists work to find a connection between the electroweak power and the strong power.
tugas quantum
TASK IV: Poynting Vector and Black-body Radiation
Anjar Sari (1017016300991)
Physic Education V
POYNTING VECTOR
Dipole Radiation, Dipole parallel to the z-axis, electric field and poynting-vector in the x-z-plane.
In physics, the Poynting vector can be thought of as representing the energy flux (in W/m2) of an electromagnetic field. It is named after its inventor John Henry Poynting.
Electromagnetic waves carry energy as they travel through empty space. There is an energy density associated with both the electric and magnetic fields. The rate of energy transport per unit area is described by the vector
which is called the Poynting vector. This expression is a vector product, and since the magnetic field is perpendicular to the electric field, the magnitude can be written
which is often called the Abraham form; here E is the electric field and H the auxiliary magnetic field. (All bold letters represent vectors.) Sometimes, an alternative definition in terms of electric field E and the magnetic field B is used, which is explained below. It is even possible to combine the displacement field D with the magnetic field B to get the Minkowski form of the Poynting vector, or use D and H to construct another. The choice has been controversial: Pfeifer et al admirably summarize the century-long dispute between proponents of the Abraham and Minkowski forms.
1. INTERPRETATION
The Poynting vector appears in Poynting's theorem, an energy-conservation law,
where Jf is the current density of free charges and u is the electromagnetic energy density,
where B is the magnetic field and D the electric displacement field.
The first term in the right-hand side represents the net electromagnetic energy flow into a small volume, while the second term represents the subtracted portion of the work done by free electrical currents that are not necessarily converted into electromagnetic energy (dissipation, heat). In this definition, bound electrical currents are not included in this term, and instead contribute to S and u.
Note that u can only be given if linear, nondispersive and uniform materials are involved, i.e., if the constitutive relations can be written as
where ε and μ are constants (which depend on the material through which the energy flows), called the permittivity and permeability, respectively, of the material.
This practically limits Poynting's theorem in this form to fields in vacuum. A generalization to dispersive materials is possible under certain circumstances at the cost of additional terms and the loss of their clear physical interpretation.
2. FORMULATION IN TERMS OF MICROSCOPIC FIELDS
In some cases, it may be more appropriate to define the Poynting vector as
where μ0 is the magnetic constant. It can be derived directly from Maxwell's equations in terms of total charge and current and the Lorentz force law only.
The corresponding form of Poynting's theorem is
where is the total current density and the energy density u is
(with the electric constant ε0).
The two alternative definitions of the Poynting vector are equivalent in vacuum or in non-magnetic materials, where . In all other cases, they differ in that and the corresponding u are purely radiative, since the dissipation term, , covers the total current, while the definition in terms of has contributions from bound currents which then lack in the dissipation term.
Since only the microscopic fields and are needed in the derivation of , assumptions about any material possibly present can be completely avoided, and Poynting's vector as well as the theorem in this definition are universally valid, in vacuum as in all kinds of material. This is especially true for the electromagnetic energy density, in contrast to the case above.
3. INVARIANCE TO ADDING A CURL OF A FIELD
Since the Poynting vector only occurs in Poynting's theorem as a divergence , the Poynting vector is arbitrary to the extent that the curl of any field F can be added, because for any field. Doing so is not common, though, and will lead to inconsistencies in a relativistic description of electromagnetic fields in terms of the stress-energy tensor.
4. EXAMPLES AND APPLICATIONS
The Poynting vector in a coaxial cable
For example, the Poynting vector within the dielectric insulator of a coaxial cable is nearly parallel to the wire axis (assuming no fields outside the cable) - so electric energy is flowing through the dielectric between the conductors. If the core conductor was replaced by a wire having significant resistance, then the Poynting vector would become tilted toward that wire, indicating that energy flows from the electromagnetic field into the wire, producing resistive Joule heating in the wire.
The Poynting vector in plane waves
In a propagating sinusoidal electromagnetic plane wave of a fixed frequency, the Poynting vector oscillates, always pointing in the direction of propagation. The time-averaged magnitude of the Poynting vector is
where is the maximum amplitude of the electric field and is the speed of light in free space. This time-averaged value is also called the irradiance or intensity I.
5. DERIVATION
In an electromagnetic plane wave, and are always perpendicular to each other and the direction of propagation. Moreover, their amplitudes are related according to
and their time and position dependences are
where is the frequency of the wave and is wave vector. The time-dependent and position magnitude of the Poynting vector is then
In the last step, we used the equality . Since the time- or space-average of is ½, it follows that
Poynting vector and radiation pressure
S divided by the square of the speed of light in free space is the density of the linear momentum of the electromagnetic field. The time-averaged intensity divided by the speed of light in free space is the radiation pressure exerted by an electromagnetic wave on the surface of a target:
BLACK BODY RADIATION
1. DEFINES
Black body spectrum the spectral distribution of energy in the temperature of the body. The higher the temperature, the greater the amount of radiation and the higher the frequency at which true maximum the maximum emission occurs.
As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.
The color (chromaticity) of black-body radiation depends on the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus.
In physics, a black body is an idealized object that absorbs all electromagnetic radiation that falls on it. No electromagnetic radiation passes through it and none is reflected. Because no light (visible electromagnetic radiation) is reflected or transmitted, the object appears black when it is cold. However, a black body emits a temperature-dependent spectrum of light. This thermal radiation from a black body is termed black-body radiation.
At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature. By the time an object is white, it is emitting substantial ultraviolet radiation. The term "black body" was introduced by Gustav Kirchhoff in 1860.
2. EXPLANATION
A typical industrial "extended
source plate" type black body.
Black-body radiation is light in thermal equilibrium with a black body, light radiation with a given temperature. It is the reference thermodynamic equilibrium state of light. Experimentally, it is established as the steady state equilibrium radiation in a rigid-walled cavity that contains a black body. There are no strictly exact black bodies in nature, but graphite is a good approximation, and a closed box with graphite walls at a steady state gives a good approximation to ideal black body radiation. A cavity that does not contain any black material body does not sustain black body radiation at equilibrium; this fact was found experimentally by Kirchhoff but its physical significance was understood neither by Kirchhoff nor by Planck.
Because light is the oscillation of a continuous electromagnetic field, the study of black-body radiation reveals how continuous fields can have a temperature, something which contradicts classical physics. Because the thermal state of light was so confusing before the advent of quantum mechanics, the 19th century arguments that light has a thermal equilibrium state were made very carefully.
An object at some fixed temperature T, like an oven, is observed to glow. The Draper point is the name given to the point at which all solids glow a dim red (about 798 K). At 1000 K, an oven looks red; at 6000 K, it looks white. No matter how the oven is constructed, so long as the oven is not too shiny, the color of the light only depends on the temperature. Since color is the directly visible measure of the wavelength, this observation means that light at different temperatures has a different distribution of energy among the different wavelengths. The amount of energy E per unit volume in wavelength λ at temperature T is called the black-body curve. Detailed experiments revealed that the black-body curve only depends on the temperature, not on the emitting body. This suggests that light does in fact come to thermal equilibrium just like anything else, that the concept of light at temperature T makes sense.
When the body is black, the absorption is obvious: the amount of light absorbed is all the light that hits the surface. For a black body much bigger than the wavelength, the light energy absorbed at any wavelength λ per unit time is strictly proportional to the black-body curve. This means that the black-body curve is the amount of light energy emitted by a black body, which justifies the name. This is Kirchhoff's law of thermal radiation: the black-body emission curve is a thermal characteristic of light, which depends only on the temperature of the walls of the cavity, provided strictly that the cavity contains some perfectly black material body and is in radiative equilibrium.
The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan-Boltzmann law. So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature.
When dealing with non-black surfaces, the deviations from ideal black-body behavior are determined by both the geometrical structure and the chemical composition, and, provided there is a radiative equilibrium with a nearly black body that is present, nearly follow Kirchhoff's Law: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body.
3. EQUATIONS GOVERNING BLACK BODIES
Planck's law of black-body radiation
Electromagnetic radiation has particle-like properties as discrete packets of energy, or quanta, called photons. The frequency of the wave is proportional to the particle's energy. Because photons are emitted and absorbed by charged particles, they act as transporters of energy. The energy per photon can be calculated from the Planck–Einstein equation:
Planck's law states that
Where:
I(ν,T) dν is the amount of energy per unit surface area per unit time per unit solid angle emitted in the frequency range between ν and ν + dν by a black body at temperature T;
h is the Planck constant;
c is the speed of light in a vacuum;
k is the Boltzmann constant;
ν is frequency of electromagnetic radiation; and
T is the temperature in kelvins.
Wien's displacement law
Wien's displacement law shows how the spectrum of black body radiation at any temperature is related to the spectrum at any other temperature. If we know the shape of the spectrum at one temperature, we can calculate the shape at any other temperature.
A consequence of Wien's displacement law is that the wavelength at which the intensity of the radiation produced by a black body is at a maximum, λmax, it is a function only of the temperature:
Where the constant, b, known as Wien's displacement constant, is equal to 2.8977685(51)×10−3 m K.
Note that the peak intensity can be expressed in terms of intensity per unit wavelength or in terms of intensity per unit frequency. The form given in this section is in terms of intensity per unit wavelength, this form given in the Planck's Law section above was in terms of intensity per unit frequency. The wavelength at which the power per unit frequency is maximised is given by
.
Stefan–Boltzmann law
This law states that amount of thermal radiation emitted per second per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature. That is
Where j* is the total energy radiated per unit area per unit time, T is the temperature in kelvins, and σ = 5.67×10−8 W m−2 K−4 is the Stefan–Boltzmann constant.
Anjar Sari (1017016300991)
Physic Education V
POYNTING VECTOR
Dipole Radiation, Dipole parallel to the z-axis, electric field and poynting-vector in the x-z-plane.
In physics, the Poynting vector can be thought of as representing the energy flux (in W/m2) of an electromagnetic field. It is named after its inventor John Henry Poynting.
Electromagnetic waves carry energy as they travel through empty space. There is an energy density associated with both the electric and magnetic fields. The rate of energy transport per unit area is described by the vector
which is called the Poynting vector. This expression is a vector product, and since the magnetic field is perpendicular to the electric field, the magnitude can be written
which is often called the Abraham form; here E is the electric field and H the auxiliary magnetic field. (All bold letters represent vectors.) Sometimes, an alternative definition in terms of electric field E and the magnetic field B is used, which is explained below. It is even possible to combine the displacement field D with the magnetic field B to get the Minkowski form of the Poynting vector, or use D and H to construct another. The choice has been controversial: Pfeifer et al admirably summarize the century-long dispute between proponents of the Abraham and Minkowski forms.
1. INTERPRETATION
The Poynting vector appears in Poynting's theorem, an energy-conservation law,
where Jf is the current density of free charges and u is the electromagnetic energy density,
where B is the magnetic field and D the electric displacement field.
The first term in the right-hand side represents the net electromagnetic energy flow into a small volume, while the second term represents the subtracted portion of the work done by free electrical currents that are not necessarily converted into electromagnetic energy (dissipation, heat). In this definition, bound electrical currents are not included in this term, and instead contribute to S and u.
Note that u can only be given if linear, nondispersive and uniform materials are involved, i.e., if the constitutive relations can be written as
where ε and μ are constants (which depend on the material through which the energy flows), called the permittivity and permeability, respectively, of the material.
This practically limits Poynting's theorem in this form to fields in vacuum. A generalization to dispersive materials is possible under certain circumstances at the cost of additional terms and the loss of their clear physical interpretation.
2. FORMULATION IN TERMS OF MICROSCOPIC FIELDS
In some cases, it may be more appropriate to define the Poynting vector as
where μ0 is the magnetic constant. It can be derived directly from Maxwell's equations in terms of total charge and current and the Lorentz force law only.
The corresponding form of Poynting's theorem is
where is the total current density and the energy density u is
(with the electric constant ε0).
The two alternative definitions of the Poynting vector are equivalent in vacuum or in non-magnetic materials, where . In all other cases, they differ in that and the corresponding u are purely radiative, since the dissipation term, , covers the total current, while the definition in terms of has contributions from bound currents which then lack in the dissipation term.
Since only the microscopic fields and are needed in the derivation of , assumptions about any material possibly present can be completely avoided, and Poynting's vector as well as the theorem in this definition are universally valid, in vacuum as in all kinds of material. This is especially true for the electromagnetic energy density, in contrast to the case above.
3. INVARIANCE TO ADDING A CURL OF A FIELD
Since the Poynting vector only occurs in Poynting's theorem as a divergence , the Poynting vector is arbitrary to the extent that the curl of any field F can be added, because for any field. Doing so is not common, though, and will lead to inconsistencies in a relativistic description of electromagnetic fields in terms of the stress-energy tensor.
4. EXAMPLES AND APPLICATIONS
The Poynting vector in a coaxial cable
For example, the Poynting vector within the dielectric insulator of a coaxial cable is nearly parallel to the wire axis (assuming no fields outside the cable) - so electric energy is flowing through the dielectric between the conductors. If the core conductor was replaced by a wire having significant resistance, then the Poynting vector would become tilted toward that wire, indicating that energy flows from the electromagnetic field into the wire, producing resistive Joule heating in the wire.
The Poynting vector in plane waves
In a propagating sinusoidal electromagnetic plane wave of a fixed frequency, the Poynting vector oscillates, always pointing in the direction of propagation. The time-averaged magnitude of the Poynting vector is
where is the maximum amplitude of the electric field and is the speed of light in free space. This time-averaged value is also called the irradiance or intensity I.
5. DERIVATION
In an electromagnetic plane wave, and are always perpendicular to each other and the direction of propagation. Moreover, their amplitudes are related according to
and their time and position dependences are
where is the frequency of the wave and is wave vector. The time-dependent and position magnitude of the Poynting vector is then
In the last step, we used the equality . Since the time- or space-average of is ½, it follows that
Poynting vector and radiation pressure
S divided by the square of the speed of light in free space is the density of the linear momentum of the electromagnetic field. The time-averaged intensity divided by the speed of light in free space is the radiation pressure exerted by an electromagnetic wave on the surface of a target:
BLACK BODY RADIATION
1. DEFINES
Black body spectrum the spectral distribution of energy in the temperature of the body. The higher the temperature, the greater the amount of radiation and the higher the frequency at which true maximum the maximum emission occurs.
As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.
The color (chromaticity) of black-body radiation depends on the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus.
In physics, a black body is an idealized object that absorbs all electromagnetic radiation that falls on it. No electromagnetic radiation passes through it and none is reflected. Because no light (visible electromagnetic radiation) is reflected or transmitted, the object appears black when it is cold. However, a black body emits a temperature-dependent spectrum of light. This thermal radiation from a black body is termed black-body radiation.
At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature. By the time an object is white, it is emitting substantial ultraviolet radiation. The term "black body" was introduced by Gustav Kirchhoff in 1860.
2. EXPLANATION
A typical industrial "extended
source plate" type black body.
Black-body radiation is light in thermal equilibrium with a black body, light radiation with a given temperature. It is the reference thermodynamic equilibrium state of light. Experimentally, it is established as the steady state equilibrium radiation in a rigid-walled cavity that contains a black body. There are no strictly exact black bodies in nature, but graphite is a good approximation, and a closed box with graphite walls at a steady state gives a good approximation to ideal black body radiation. A cavity that does not contain any black material body does not sustain black body radiation at equilibrium; this fact was found experimentally by Kirchhoff but its physical significance was understood neither by Kirchhoff nor by Planck.
Because light is the oscillation of a continuous electromagnetic field, the study of black-body radiation reveals how continuous fields can have a temperature, something which contradicts classical physics. Because the thermal state of light was so confusing before the advent of quantum mechanics, the 19th century arguments that light has a thermal equilibrium state were made very carefully.
An object at some fixed temperature T, like an oven, is observed to glow. The Draper point is the name given to the point at which all solids glow a dim red (about 798 K). At 1000 K, an oven looks red; at 6000 K, it looks white. No matter how the oven is constructed, so long as the oven is not too shiny, the color of the light only depends on the temperature. Since color is the directly visible measure of the wavelength, this observation means that light at different temperatures has a different distribution of energy among the different wavelengths. The amount of energy E per unit volume in wavelength λ at temperature T is called the black-body curve. Detailed experiments revealed that the black-body curve only depends on the temperature, not on the emitting body. This suggests that light does in fact come to thermal equilibrium just like anything else, that the concept of light at temperature T makes sense.
When the body is black, the absorption is obvious: the amount of light absorbed is all the light that hits the surface. For a black body much bigger than the wavelength, the light energy absorbed at any wavelength λ per unit time is strictly proportional to the black-body curve. This means that the black-body curve is the amount of light energy emitted by a black body, which justifies the name. This is Kirchhoff's law of thermal radiation: the black-body emission curve is a thermal characteristic of light, which depends only on the temperature of the walls of the cavity, provided strictly that the cavity contains some perfectly black material body and is in radiative equilibrium.
The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan-Boltzmann law. So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature.
When dealing with non-black surfaces, the deviations from ideal black-body behavior are determined by both the geometrical structure and the chemical composition, and, provided there is a radiative equilibrium with a nearly black body that is present, nearly follow Kirchhoff's Law: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body.
3. EQUATIONS GOVERNING BLACK BODIES
Planck's law of black-body radiation
Electromagnetic radiation has particle-like properties as discrete packets of energy, or quanta, called photons. The frequency of the wave is proportional to the particle's energy. Because photons are emitted and absorbed by charged particles, they act as transporters of energy. The energy per photon can be calculated from the Planck–Einstein equation:
Planck's law states that
Where:
I(ν,T) dν is the amount of energy per unit surface area per unit time per unit solid angle emitted in the frequency range between ν and ν + dν by a black body at temperature T;
h is the Planck constant;
c is the speed of light in a vacuum;
k is the Boltzmann constant;
ν is frequency of electromagnetic radiation; and
T is the temperature in kelvins.
Wien's displacement law
Wien's displacement law shows how the spectrum of black body radiation at any temperature is related to the spectrum at any other temperature. If we know the shape of the spectrum at one temperature, we can calculate the shape at any other temperature.
A consequence of Wien's displacement law is that the wavelength at which the intensity of the radiation produced by a black body is at a maximum, λmax, it is a function only of the temperature:
Where the constant, b, known as Wien's displacement constant, is equal to 2.8977685(51)×10−3 m K.
Note that the peak intensity can be expressed in terms of intensity per unit wavelength or in terms of intensity per unit frequency. The form given in this section is in terms of intensity per unit wavelength, this form given in the Planck's Law section above was in terms of intensity per unit frequency. The wavelength at which the power per unit frequency is maximised is given by
.
Stefan–Boltzmann law
This law states that amount of thermal radiation emitted per second per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature. That is
Where j* is the total energy radiated per unit area per unit time, T is the temperature in kelvins, and σ = 5.67×10−8 W m−2 K−4 is the Stefan–Boltzmann constant.
TASK III: Analysis Electromagnetic Radiation with Maxwell Theory
Anjar Sari (1017016300991)
Physic Education V
ANALYSIS ELECTROMAGNETIC RADIATION
1. MAXWELL'S EQUATIONS
Maxwell's equations are a set of four partial differential equations that relate the electric and magnetic fields to their sources, charge density and current density. These equations can be combined to show that light is an electromagnetic wave. Individually, the equations are known as Gauss's law, Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction. The set of equations is named after James Clerk Maxwell.
These four equations, together with the Lorentz force law are the complete set of laws of classical electromagnetism. The Lorentz force law itself was actually derived by Maxwell under the name of "Equation for Electromotive Force" and was one of an earlier set of eight equations by Maxwell.
Conceptual description
This section will conceptually describe each of the four Maxwell's equations, and also how they link together to explain the origin of electromagnetic radiation such as light. The exact equations are set out in later sections of this entry.
• Gauss's law relates electric charge contained within a closed surface (Gaussian surface) to the surrounding electric field. It describes with mathematical clarity how the divergence of an electrical field is affected by charges (electric field lines diverge from positive charges and are drawn towards negative charges). It also states that the total electric flux through a Gaussian surface is unrelated to the shape and size of that surface.
• Gauss's law for magnetism states that the total magnetic flux through a Gaussian surface is zero. It is equivalent to saying that the magnetic field is a solenoidal vector field. This is due to real world magnetic charges coming in pairs (referred to as dipoles), with the two charges giving rise to opposite magnetic field divergences which cancel each other out. The theoretical single magnetic charge is referred to as a magnetic monopole. Magnetic monopoles have never been observed, but if they do exist, this law would need to be modified.
• The Maxwell equation that is known as 'Faraday's law' was so named by Oliver Heaviside. It describes how a changing magnetic field is related to the induced electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators. It should be noted however that this particular equation only caters for the time varying aspect of electromagnetic induction, and not for the motionally induced aspect, and that it takes on a different mathematical form than Michael Faraday's original law. In the original Faraday's law of induction, both aspects of electromagnetic induction are catered for.
• Ampère's law with Maxwell's correction states that magnetic fields can be generated in two ways: By electrical current (this was the original "Ampère's law") and by changing electric fields. The idea that a magnetic field can be induced by a changing electric field follows from the modern concept of displacement current which was introduced to maintain the solenoidal nature of Ampère's law in a vacuum capacitor circuit. This modern displacement current concept has the same mathematical form as Maxwell's original displacement current. Maxwell's current applies to the polarization current in a dielectric medium, and it sits adjacent to the modern displacement current in Ampère's law.
Maxwell's correction to Ampère's law was particularly important. In 1864, Maxwell derived the electromagnetic wave equation by linking the displacement current to the time-varying electric field that is associated with electromagnetic induction. This is described in his A Dynamical Theory of the Electromagnetic Field, where he wrote:
"The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws."
Formulation in terms of free charge and current
Name Differential form
Integral form
Gauss's law
Gauss's law for magnetism
Maxwell–Faraday equation
(Faraday's law of induction)
Ampère's circuital law
(with Maxwell's correction)
Formulation in terms of total charge and current
Name Differential form Integral form
Gauss's law
Gauss's law for magnetism
Maxwell–Faraday equation
(Faraday's law of induction)
Ampère's circuital law
(with Maxwell's correction)
Maxwell's equations in terms of E and B for linear materials
Substituting in the constitutive relations above, Maxwell's equations in linear, dispersionless, time-invariant materials (differential form only) are:
These are formally identical to the general formulation in terms of E and B (given above), except that the permittivity of free space was replaced with the permittivity of the material (see also displacement field, electric susceptibility and polarization density), the permeability of free space was replaced with the permeability of the material (see also magnetization, magnetic susceptibility and magnetic field), and only free charges and currents are included (instead of all charges and currents). Unless that material is homogeneous in space, ε and μ cannot be factored out of the derivative expressions on the left-hand sides.
Electromagnetic radiation (sometimes abbreviated EMR) is a ubiquitous phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It consists of electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according to the frequency of its wave; these types include (in order of increasing frequency and decreasing wavelength): radio waves, microwaves, terahertz radiation, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. A small and somewhat variable window of frequencies is sensed by the eyes of various organisms; this is what we call the visible spectrum, or light.
Electromagnetic waves were first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.
According to Maxwell's equations, a spatially-varying electric field generates a time-varying magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave.
A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.
Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized wave propagating from right to left. The electric field is in a vertical plane, the magnetic field in a horizontal plane.
The physics of electromagnetic radiation is electrodynamics, a subfield of electromagnetism. Electric and magnetic fields obey the properties of superposition so that a field due to any particular particle or time-varying electric or magnetic field will contribute to the fields present in the same space due to other causes: as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For instance, a travelling EM wave incident on an atomic structure induces oscillation in the atoms of that structure, thereby causing them to emit their own EM waves, emissions which alter the impinging wave through interference. These properties cause various phenomena including refraction and diffraction.
Since light is an oscillation it is not affected by travelling through static electric or magnetic fields in a linear medium such as a vacuum. However in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields — these interactions include the Faraday effect and the Kerr effect.
In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. Light disperses into a visible spectrum as light is shone through a prism because of the wavelength dependent refractive index of the prism material (Dispersion).
EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality). Both wave and particle characteristics have been confirmed in a large number of experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. Upon absorption the quantum nature of the light leads to clearly non-uniform deposition of energy.
There are experiments in which the wave and particle natures of electromagnetic waves appear in the same experiment, such as the diffraction of a single photon. When a single photon is sent through two slits, it passes through both of them interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once. Similar self-interference is observed when a single photon is sent into a Michelson interferometer or other interferometers.
Electromagnetic spectrum
Generally, EM radiation (the designation 'radiation' excludes static electric and magnetic and near fields) is classified by wavelength into radio, microwave, infrared, the visible region we perceive as light, ultraviolet, X-rays and gamma rays. Arbitrary electromagnetic waves can always be expressed by Fourier analysis in terms of sinusoidal monochromatic waves which can be classified into these regions of the spectrum.
The behavior of EM radiation depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. When EM radiation interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. Spectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. Detailed information about the physical properties of objects, gases, or even stars can be obtained from this type of device. It is widely used in astrophysics. For example, hydrogen atoms emit radio waves of wavelength 21.12 cm.
2. WAVE EQUATION ANALYSIS
Wave equation models a pile as a series of masses connected by springs and a hammer blow as a compressive stress wave which travels trough the pile. General form of wave equation
analysis is:
where u is longitudinal displacement of a point, E is modulus of elasticity, ρ is density, t is time, x is longitudinal direction, and Rd is soil resistance.
Wave equation analysis programs are utilized more reliable pile driving result. In this paper, the MICROWAVE is conducted. The wave equation analysis will provide driving system of pile-hammer combination suitability, driving stresses, as well as pile drivability or adequacy of the driving system to achieve required bearing capacity.
The wave equation is usually used to investigate bearing capacity graph which is a plot of ultimate soil resistance versus set. Another is to give information about equipment compatibility-solutions for determining the type of hammer. A pile-hammer system is a set of discrete element which can be solved by using of springs and dampers. Smith (1960) proposed five basic equations for wave equation
analysis:
Dm,t = Dm,t-l + Vm,t-l.dt
where: Dm,t = displacement of element m when t = t
Dm,t-1 = displacement of element m when t = t-1
Cm,t = spring compression of element m when t = t
Km = pile’s spring constant include cap, capblock, and cushion
Fm,t = spring force of element m
R’ = soil resistance, include damping effect
Rm,t = final force resultant
Vm,t = velocity of element m when t = t
Wm = weight of element m
g = gravitation
Δt = time interval
Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. If you inspect Maxwell's equations without sources (charges or currents) then you will find that, along with the possibility of nothing happening, the theory will also admit nontrivial solutions of changing electric and magnetic fields. Beginning with Maxwell's equations for free space:
where
is a vector differential operator (see Del).
One solution,
,
is trivial.
To see the more interesting one, we utilize vector identities, which work for any vector, as follows:
To see how we can use this take the curl of equation (2):
Evaluating the left hand side:
where we simplified the above by using equation (1).
Evaluate the right hand side:
Equations (6) and (7) are equal, so this results in a vector-valued differential equation for the electric field, namely
Applying a similar pattern results in similar differential equation for the magnetic field:
.
These differential equations are equivalent to the wave equation:
where
c0 is the speed of the wave in free space and
f describes a displacement
Or more simply:
where is d'Alembertian:
Notice that in the case of the electric and magnetic fields, the speed is:
Which, as it turns out, is the speed of light in free space. Maxwell's equations have unified the permittivity of free space ε0, the permeability of free space μ0, and the speed of light itself, c0. Before this derivation it was not known that there was such a strong relationship between light and electricity and magnetism.
But these are only two equations and we started with four, so there is still more information pertaining to these waves hidden within Maxwell's equations. Let's consider a generic vector wave for the electric field.
Here is the constant amplitude, f is any second differentiable function, is a unit vector in the direction of propagation, and is a position vector. We observe that is a generic solution to the wave equation. In other words
,
for a generic wave traveling in the direction.
This form will satisfy the wave equation, but will it satisfy all of Maxwell's equations, and with what corresponding magnetic field?
The first of Maxwell's equations implies that electric field is orthogonal to the direction the wave propagates.
The second of Maxwell's equations yields the magnetic field. The remaining equations will be satisfied by this choice of .
Not only are the electric and magnetic field waves traveling at the speed of light, but they have a special restricted orientation and proportional magnitudes, E0 = c0B0, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as .
From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left; but this picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization.
Anjar Sari (1017016300991)
Physic Education V
ANALYSIS ELECTROMAGNETIC RADIATION
1. MAXWELL'S EQUATIONS
Maxwell's equations are a set of four partial differential equations that relate the electric and magnetic fields to their sources, charge density and current density. These equations can be combined to show that light is an electromagnetic wave. Individually, the equations are known as Gauss's law, Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction. The set of equations is named after James Clerk Maxwell.
These four equations, together with the Lorentz force law are the complete set of laws of classical electromagnetism. The Lorentz force law itself was actually derived by Maxwell under the name of "Equation for Electromotive Force" and was one of an earlier set of eight equations by Maxwell.
Conceptual description
This section will conceptually describe each of the four Maxwell's equations, and also how they link together to explain the origin of electromagnetic radiation such as light. The exact equations are set out in later sections of this entry.
• Gauss's law relates electric charge contained within a closed surface (Gaussian surface) to the surrounding electric field. It describes with mathematical clarity how the divergence of an electrical field is affected by charges (electric field lines diverge from positive charges and are drawn towards negative charges). It also states that the total electric flux through a Gaussian surface is unrelated to the shape and size of that surface.
• Gauss's law for magnetism states that the total magnetic flux through a Gaussian surface is zero. It is equivalent to saying that the magnetic field is a solenoidal vector field. This is due to real world magnetic charges coming in pairs (referred to as dipoles), with the two charges giving rise to opposite magnetic field divergences which cancel each other out. The theoretical single magnetic charge is referred to as a magnetic monopole. Magnetic monopoles have never been observed, but if they do exist, this law would need to be modified.
• The Maxwell equation that is known as 'Faraday's law' was so named by Oliver Heaviside. It describes how a changing magnetic field is related to the induced electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators. It should be noted however that this particular equation only caters for the time varying aspect of electromagnetic induction, and not for the motionally induced aspect, and that it takes on a different mathematical form than Michael Faraday's original law. In the original Faraday's law of induction, both aspects of electromagnetic induction are catered for.
• Ampère's law with Maxwell's correction states that magnetic fields can be generated in two ways: By electrical current (this was the original "Ampère's law") and by changing electric fields. The idea that a magnetic field can be induced by a changing electric field follows from the modern concept of displacement current which was introduced to maintain the solenoidal nature of Ampère's law in a vacuum capacitor circuit. This modern displacement current concept has the same mathematical form as Maxwell's original displacement current. Maxwell's current applies to the polarization current in a dielectric medium, and it sits adjacent to the modern displacement current in Ampère's law.
Maxwell's correction to Ampère's law was particularly important. In 1864, Maxwell derived the electromagnetic wave equation by linking the displacement current to the time-varying electric field that is associated with electromagnetic induction. This is described in his A Dynamical Theory of the Electromagnetic Field, where he wrote:
"The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws."
Formulation in terms of free charge and current
Name Differential form
Integral form
Gauss's law
Gauss's law for magnetism
Maxwell–Faraday equation
(Faraday's law of induction)
Ampère's circuital law
(with Maxwell's correction)
Formulation in terms of total charge and current
Name Differential form Integral form
Gauss's law
Gauss's law for magnetism
Maxwell–Faraday equation
(Faraday's law of induction)
Ampère's circuital law
(with Maxwell's correction)
Maxwell's equations in terms of E and B for linear materials
Substituting in the constitutive relations above, Maxwell's equations in linear, dispersionless, time-invariant materials (differential form only) are:
These are formally identical to the general formulation in terms of E and B (given above), except that the permittivity of free space was replaced with the permittivity of the material (see also displacement field, electric susceptibility and polarization density), the permeability of free space was replaced with the permeability of the material (see also magnetization, magnetic susceptibility and magnetic field), and only free charges and currents are included (instead of all charges and currents). Unless that material is homogeneous in space, ε and μ cannot be factored out of the derivative expressions on the left-hand sides.
Electromagnetic radiation (sometimes abbreviated EMR) is a ubiquitous phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It consists of electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according to the frequency of its wave; these types include (in order of increasing frequency and decreasing wavelength): radio waves, microwaves, terahertz radiation, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. A small and somewhat variable window of frequencies is sensed by the eyes of various organisms; this is what we call the visible spectrum, or light.
Electromagnetic waves were first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.
According to Maxwell's equations, a spatially-varying electric field generates a time-varying magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave.
A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.
Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized wave propagating from right to left. The electric field is in a vertical plane, the magnetic field in a horizontal plane.
The physics of electromagnetic radiation is electrodynamics, a subfield of electromagnetism. Electric and magnetic fields obey the properties of superposition so that a field due to any particular particle or time-varying electric or magnetic field will contribute to the fields present in the same space due to other causes: as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For instance, a travelling EM wave incident on an atomic structure induces oscillation in the atoms of that structure, thereby causing them to emit their own EM waves, emissions which alter the impinging wave through interference. These properties cause various phenomena including refraction and diffraction.
Since light is an oscillation it is not affected by travelling through static electric or magnetic fields in a linear medium such as a vacuum. However in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields — these interactions include the Faraday effect and the Kerr effect.
In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. Light disperses into a visible spectrum as light is shone through a prism because of the wavelength dependent refractive index of the prism material (Dispersion).
EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality). Both wave and particle characteristics have been confirmed in a large number of experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. Upon absorption the quantum nature of the light leads to clearly non-uniform deposition of energy.
There are experiments in which the wave and particle natures of electromagnetic waves appear in the same experiment, such as the diffraction of a single photon. When a single photon is sent through two slits, it passes through both of them interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once. Similar self-interference is observed when a single photon is sent into a Michelson interferometer or other interferometers.
Electromagnetic spectrum
Generally, EM radiation (the designation 'radiation' excludes static electric and magnetic and near fields) is classified by wavelength into radio, microwave, infrared, the visible region we perceive as light, ultraviolet, X-rays and gamma rays. Arbitrary electromagnetic waves can always be expressed by Fourier analysis in terms of sinusoidal monochromatic waves which can be classified into these regions of the spectrum.
The behavior of EM radiation depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. When EM radiation interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. Spectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. Detailed information about the physical properties of objects, gases, or even stars can be obtained from this type of device. It is widely used in astrophysics. For example, hydrogen atoms emit radio waves of wavelength 21.12 cm.
2. WAVE EQUATION ANALYSIS
Wave equation models a pile as a series of masses connected by springs and a hammer blow as a compressive stress wave which travels trough the pile. General form of wave equation
analysis is:
where u is longitudinal displacement of a point, E is modulus of elasticity, ρ is density, t is time, x is longitudinal direction, and Rd is soil resistance.
Wave equation analysis programs are utilized more reliable pile driving result. In this paper, the MICROWAVE is conducted. The wave equation analysis will provide driving system of pile-hammer combination suitability, driving stresses, as well as pile drivability or adequacy of the driving system to achieve required bearing capacity.
The wave equation is usually used to investigate bearing capacity graph which is a plot of ultimate soil resistance versus set. Another is to give information about equipment compatibility-solutions for determining the type of hammer. A pile-hammer system is a set of discrete element which can be solved by using of springs and dampers. Smith (1960) proposed five basic equations for wave equation
analysis:
Dm,t = Dm,t-l + Vm,t-l.dt
where: Dm,t = displacement of element m when t = t
Dm,t-1 = displacement of element m when t = t-1
Cm,t = spring compression of element m when t = t
Km = pile’s spring constant include cap, capblock, and cushion
Fm,t = spring force of element m
R’ = soil resistance, include damping effect
Rm,t = final force resultant
Vm,t = velocity of element m when t = t
Wm = weight of element m
g = gravitation
Δt = time interval
Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. If you inspect Maxwell's equations without sources (charges or currents) then you will find that, along with the possibility of nothing happening, the theory will also admit nontrivial solutions of changing electric and magnetic fields. Beginning with Maxwell's equations for free space:
where
is a vector differential operator (see Del).
One solution,
,
is trivial.
To see the more interesting one, we utilize vector identities, which work for any vector, as follows:
To see how we can use this take the curl of equation (2):
Evaluating the left hand side:
where we simplified the above by using equation (1).
Evaluate the right hand side:
Equations (6) and (7) are equal, so this results in a vector-valued differential equation for the electric field, namely
Applying a similar pattern results in similar differential equation for the magnetic field:
.
These differential equations are equivalent to the wave equation:
where
c0 is the speed of the wave in free space and
f describes a displacement
Or more simply:
where is d'Alembertian:
Notice that in the case of the electric and magnetic fields, the speed is:
Which, as it turns out, is the speed of light in free space. Maxwell's equations have unified the permittivity of free space ε0, the permeability of free space μ0, and the speed of light itself, c0. Before this derivation it was not known that there was such a strong relationship between light and electricity and magnetism.
But these are only two equations and we started with four, so there is still more information pertaining to these waves hidden within Maxwell's equations. Let's consider a generic vector wave for the electric field.
Here is the constant amplitude, f is any second differentiable function, is a unit vector in the direction of propagation, and is a position vector. We observe that is a generic solution to the wave equation. In other words
,
for a generic wave traveling in the direction.
This form will satisfy the wave equation, but will it satisfy all of Maxwell's equations, and with what corresponding magnetic field?
The first of Maxwell's equations implies that electric field is orthogonal to the direction the wave propagates.
The second of Maxwell's equations yields the magnetic field. The remaining equations will be satisfied by this choice of .
Not only are the electric and magnetic field waves traveling at the speed of light, but they have a special restricted orientation and proportional magnitudes, E0 = c0B0, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as .
From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left; but this picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization.
TAKS II: Undulation Theory
Anjar Sari (1017016300991)
Physic Education V
UNDULATION THEORY
To estimate wavelength of undulator radiation apply special relativity twice
1. Moving system: undulator period appears shortened by length contraction emission of dipole radiation with wavelength
2. Lorentz transformation into lab. System
Comparison of Quantum Laser and Free-Electron Laser
→ quantized energy levels
→ energy pump to create population inversion
→ stimulated emission of radiation
→ optical resonator
→ electron energy not quantized
→ energy source: kinetic energy of beam
→ stimulated emission of radiation
→ optical resonator or SASE
Undulator Radiation
Electron motion in undulator
Lorentz transformation into moving coordinate system
Power of undulator radiation
Line shape of undulator radiation
Undulator field approx. Harmonic
Plane
Total relativistic energy of the electron
Firs oder solution:
Electron travels on a sine-like trajectory
Undulator parameter
Transverse velocity and maximum divergence angle of trajectory
Synchrotron radiation is emitted inside a cone with opening angle
Undulator: particle trajectory stays within this cone
Note: Radiation field amplitudes from various sections of andulator trajectory overlap
and interfere =>radiation is nearly monochromatic (fundamental frequency plus higher
harmonics).
Motion in second order
On sine-trajectory:
Insert for the first-order solution, then the average z velocity is:
Note: z velocity oscillates about the average
with
Electron trajectory in second order
Lorentz transformation into moving coordinate system
Coordinate system (x*, y*, z*) moving with average z velocity of electron:
Mainly transverse harmonic oscillation with frequency
Small superimposed longitudinal oscillation generates odd higher harmonics in moving system: electron emits dipole radiation
Lorentz transformation of photon energy
Use and
Wavelength of undulator radiation
Undulator radiation of an electron with v = 0.9 c
Radiation power in moving system computed with Larmor formula
Radiation power in laboratory system is the same:
Line shape of undulator radiation
Electron passing an undulator with Nu periods produces wave train with Nu oscillations.
Spectral intensity :
Anjar Sari (1017016300991)
Physic Education V
UNDULATION THEORY
To estimate wavelength of undulator radiation apply special relativity twice
1. Moving system: undulator period appears shortened by length contraction emission of dipole radiation with wavelength
2. Lorentz transformation into lab. System
Comparison of Quantum Laser and Free-Electron Laser
→ quantized energy levels
→ energy pump to create population inversion
→ stimulated emission of radiation
→ optical resonator
→ electron energy not quantized
→ energy source: kinetic energy of beam
→ stimulated emission of radiation
→ optical resonator or SASE
Undulator Radiation
Electron motion in undulator
Lorentz transformation into moving coordinate system
Power of undulator radiation
Line shape of undulator radiation
Undulator field approx. Harmonic
Plane
Total relativistic energy of the electron
Firs oder solution:
Electron travels on a sine-like trajectory
Undulator parameter
Transverse velocity and maximum divergence angle of trajectory
Synchrotron radiation is emitted inside a cone with opening angle
Undulator: particle trajectory stays within this cone
Note: Radiation field amplitudes from various sections of andulator trajectory overlap
and interfere =>radiation is nearly monochromatic (fundamental frequency plus higher
harmonics).
Motion in second order
On sine-trajectory:
Insert for the first-order solution, then the average z velocity is:
Note: z velocity oscillates about the average
with
Electron trajectory in second order
Lorentz transformation into moving coordinate system
Coordinate system (x*, y*, z*) moving with average z velocity of electron:
Mainly transverse harmonic oscillation with frequency
Small superimposed longitudinal oscillation generates odd higher harmonics in moving system: electron emits dipole radiation
Lorentz transformation of photon energy
Use and
Wavelength of undulator radiation
Undulator radiation of an electron with v = 0.9 c
Radiation power in moving system computed with Larmor formula
Radiation power in laboratory system is the same:
Line shape of undulator radiation
Electron passing an undulator with Nu periods produces wave train with Nu oscillations.
Spectral intensity :
tugas Quantum
TASK I: Wave Analysis
Anjar Sari (1017016300991)
Physic Education V
WAVE
Energy can be transmitted from one place to another in a variety of ways. Suppose we wish supply energy to about in the center of a lake from a position on the sheer, with the provision that the precise from in which the energy arrives does not matter.
A wave is a disturbance that propagates through space and time, usually with transference of energy. A mechanical wave is a wave that propagates or travels through a medium due to the restoring forces it produces upon deformation. There also exist waves capable of traveling through a vacuum, including electromagnetic radiation and probably gravitational radiation.
1. DEFINITIONS
Agreeing on a single, all-encompassing definition for the term wave is non-trivial. A vibration can be defined as a back-and-forth motion around a reference value. However, a vibration is not necessarily a wave. Defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible.
The term is often understood intuitively as the transport of disturbances in space, not associated with motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium .However, this notion is problematic for a standing wave (for example, a wave on a string), where energy is moving in both directions equally, or for electromagnetic / light waves in a vacuum, where the concept of medium does not apply. There are water waves in the ocean; light waves from the sun; microwaves inside the microwave oven; radio waves transmitted to the radio; and sound waves from the radio, telephone, and voices.
It may be seen that the description of waves is accompanied by a heavy reliance on physical origin when describing any specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic wave-like transfer / transformation of vibratory energy. Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as distinct from optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved.
2. MATHEMATICAL DESCRIPTION
Four related quantities are useful in describing periodic waves:
1. the waves velocity V, which is the distance through which each waves moves per second
2. the waves length (Greek letter lambda), which is the distance between adjacent crests or troughs
3. the frequency f which is the number of waves that pass a given point second
4. the amplitude A of a waves refer to the maximum displacement from the normal position of the particles which oscillate back and forta as the waves travels by
A wave is represented mathematically by a variation in some quantity that is described as a function of both position and time. For a transverse wave on a guitar string, the function specifies the displacement of each point on the string from its equilibrium position. If the string is oriented a long the x-axis and the displacement of any point the string in the ± y-dissection, the waves is described by a function of two variables y (x,t).
Two analyze the standing waves mathematically, we represent the two waves by:
Hence the resultant my be written
In a periodic wave one pulse follows another in regular succession. Sound waves, water waves, and light waves are almost always periodic although in each care a different quantity waves as the waves passer
At any given point, the waves repents is tell after a time T called the periodic. The inverse of periodic is the frequency f.
(is unit Hz = s-1)
In the case of a periodic function F with period λ, that is, F(x + λ − vt) = F(x − vt), the periodicity of F in space means that a snapshot of the wave at a given time t finds the wave varying periodically in space with period λ (sometimes called the wavelength of the wave). In a similar fashion, this periodicity of F implies a periodicity in time as well: F(x − v(t + T)) = F(x − vt) provided vT = λ, so an observation of the wave at a fixed location x finds the wave undulating periodically in time with period T = λ/v.
Anjar Sari (1017016300991)
Physic Education V
WAVE
Energy can be transmitted from one place to another in a variety of ways. Suppose we wish supply energy to about in the center of a lake from a position on the sheer, with the provision that the precise from in which the energy arrives does not matter.
A wave is a disturbance that propagates through space and time, usually with transference of energy. A mechanical wave is a wave that propagates or travels through a medium due to the restoring forces it produces upon deformation. There also exist waves capable of traveling through a vacuum, including electromagnetic radiation and probably gravitational radiation.
1. DEFINITIONS
Agreeing on a single, all-encompassing definition for the term wave is non-trivial. A vibration can be defined as a back-and-forth motion around a reference value. However, a vibration is not necessarily a wave. Defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible.
The term is often understood intuitively as the transport of disturbances in space, not associated with motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium .However, this notion is problematic for a standing wave (for example, a wave on a string), where energy is moving in both directions equally, or for electromagnetic / light waves in a vacuum, where the concept of medium does not apply. There are water waves in the ocean; light waves from the sun; microwaves inside the microwave oven; radio waves transmitted to the radio; and sound waves from the radio, telephone, and voices.
It may be seen that the description of waves is accompanied by a heavy reliance on physical origin when describing any specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic wave-like transfer / transformation of vibratory energy. Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as distinct from optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved.
2. MATHEMATICAL DESCRIPTION
Four related quantities are useful in describing periodic waves:
1. the waves velocity V, which is the distance through which each waves moves per second
2. the waves length (Greek letter lambda), which is the distance between adjacent crests or troughs
3. the frequency f which is the number of waves that pass a given point second
4. the amplitude A of a waves refer to the maximum displacement from the normal position of the particles which oscillate back and forta as the waves travels by
A wave is represented mathematically by a variation in some quantity that is described as a function of both position and time. For a transverse wave on a guitar string, the function specifies the displacement of each point on the string from its equilibrium position. If the string is oriented a long the x-axis and the displacement of any point the string in the ± y-dissection, the waves is described by a function of two variables y (x,t).
Two analyze the standing waves mathematically, we represent the two waves by:
Hence the resultant my be written
In a periodic wave one pulse follows another in regular succession. Sound waves, water waves, and light waves are almost always periodic although in each care a different quantity waves as the waves passer
At any given point, the waves repents is tell after a time T called the periodic. The inverse of periodic is the frequency f.
(is unit Hz = s-1)
In the case of a periodic function F with period λ, that is, F(x + λ − vt) = F(x − vt), the periodicity of F in space means that a snapshot of the wave at a given time t finds the wave varying periodically in space with period λ (sometimes called the wavelength of the wave). In a similar fashion, this periodicity of F implies a periodicity in time as well: F(x − v(t + T)) = F(x − vt) provided vT = λ, so an observation of the wave at a fixed location x finds the wave undulating periodically in time with period T = λ/v.
matkul biologi semester 2
Nama : Anjar Sari
NIM : 107016300991
Prodi : Fisika
Semester : III (Tiga)
Jawaban Quis II
Biologi Dasar I
1. Dalam hal apakah berbagai macam membran sel eukariotik berbeda?
Jawaban: B. Protein bersifat unik untuk setiap membran.
Alasan : Protein merupakan bahan penyusun utama membran. Para Saintis telah menemukan bahwa membran ternyata tersusun atas lipid dan protein.
Protein membran memiliki daerah hidrofobik dan hidrofilik. Protein ini amfibatik, seperti pasangan fosfolipidnya dalam membran. Jika protein melapisi permukaan membran, bagian-bagian hidrofibiknya akan berada dalam lingkungan equeos.
Pada tahun 1972, S.J. Singer dan G. Nicolson juga menganjurkan macam-macam model suatu membran karena adanya protein pada suatu lokasi yang sesuai dengan karakter amfipatiknya.
Selain itu juga terdapat populasi utama protein membran. Protein integral, umumnya merupakan protein transmembran dan protein porferal, merupakan protein yang secara longgar terikat pada permukaan membran. Dan protein itu sendiri dapat berpindah secara acak di dalam membran.
2. Menurut model mozaik fluida struktur membran, protein membran sebagian besar...
Jawaban: C. Tertanam dalam bilayer lipid
Alasan : Karena membran merupakan klokase banyak protein berbeda-beda yang tertanam dalam matrik fluida bilayer lipid, bilayer fosfolip merupakan penyusun utama membran. Bilayer fosfolipid diantara dua lapisan protein glabular (terbentuk seperti bola). Bilayer ini merupakan fluida penyusun utama membran tersebut, tetapi protein menentukan sebagian besar fungsi spesifik membran.
3. Yang mana dan faktor apa berikut yang cenderung meningkatkan fluiditas membran?
Jawaban: A. Proposisi fosfolipid tak jenuh yang semakin besar.
Alasan : Karena ekor hidro membran tak jenuh fosfolipid memiliki lekukan atau kekusutan yang menghalangi molekul tersusun rapat sehingga meningkatkan fluiditas membran.
Membran tetap berwujud fluida pada suhu lebih rendah jika membran itu banyak mengandung fosfolipid dengan ekor hidrokarbon tak jenuh. Karena ada kekusutan di tempat ikatan gandanya, hidrokarbon tak jenuh tersusun serapat hidrokarbon jenuh.
4. Yang mana dari proses berikut yang mencakup semua yang lain dalam daftar berikut?
Jawaban: D. Transpor pasif
Alasan : Karena transpor pasif merupakan difusi melintas suatu membran. Suatu zat akan berdifusi dari suatu tempat yang lain yang lebih pekat ke tempat yang kurang pekat. Jika suatu membran permeabel terhadap warna, misalkan suatu membran yang memisahkan air murni dari larutan zat pewarna dalam air. Setiap pewarna akan berbaur secara acak, dan tetap bergerak. Mebran itu permeabel selektif sehingga mempengaruhi laju difusi berbagai malekul.
5. Didasarkan pada model penyerapan sukrosa pada gambar 8.17 yang mana dari percobaan berikut yang akan meningkatkan laju transpor sukrosa ke dalam sel?
Jawaban: B. Penurunan pH ekstraseluler.
Alasan : Karena transpor sukrosa yang masuk ke dalam sel dan satu protein dikembalikannya ion hidrogen dengan transpor tersebut. Protein ini dapat mentranslokasikan sukrosa ke dalam sel melawan gradien konsentrasi tetapi hanya jika molekul sukrosanya berpindah bersamaan dengan ion hodrogen yang menggunakan protein transpor sekutu sebagai jalan untuk berdifusi menuruni gradien konsentrasi yang dipertahankan oleh pompa proton.
Pertanyaan no 6 s.d 10
Sel buatan yang terdiri atas larutan equeos yang dibatasi mebran permeabel selektif dicelupkan ke dalam suatu labu yang berisi larutan yang berbeda. Membran ini permeabel terhadap air dan gula sederhana glukosa serta fruktosa tetapi sama sekali tidak permeabel terhadap sukrosa disakarida
Lingkungan
Sel
0,03 M sukrosa 0,01 M sukrosa
0,02 M glukosa 0,01 M glukosa
0,01 M fruktosa
6. Larutan mana yang akan memperlihatkan selisih difusi ke luar sel?
Jawaba: Fruktosa
Alasan : Frustosa ini diibaratkan sebagai lingkungan. Sel itu akan menyerap fruktosa yang ada dalam lingkungan dan masuk ke dalam sel. Dinding kaku yang ada di sel akan membantu penyerapan sukrosa.
7. Larutan mana yang akan memperlihatkan selisih difusi ke luar sel?
Jawaban: Glukosa
Alasan : Glukosa ini akan membantu menyeimbangkan sel terhadap lingkungan.
8. Larutan mana yang akan memperlihatkan selisih difusi ke dalam sel?
Jawaban: Kandungan sel
Alasan : Jika suatu sel dicelupkan dalam lingkungan yang isotonik terhadap sel tersebut, tidak akan ada selisih perpindahan air melintasi membran tersebut. Air melintasi membran, tetapi pada laju sama pada kedua arah. Jika sel tersebut dipindahkan ke dalam larutan hipertonik terhadap sel tersebut. Sel ini akan kehilangkan air yang berpindah ke dalam ke lingkungan, mengkerut dan mungkin saja mati.
Jika kita menempatkan sel tersebut ke dalam larutan yang hipotonik terdapat sel itu, air akan masuk lebih cepat daripada yang meninggalkannya.
9. Ke arah mana akan terjadi selisih perpindahan osmotik air?
Jawaban: Ke dalam
Alasan : Apabila sel berada dalam larutan hipotinik (misalkan direndam dalam air), akan membantu mempertahankan keseimbangan air sel tersebut. Sel ini kemudian akan membengkak hanya sampai pada ukuran tertentu sebelum dinding ini mengarahkan tekanan balik pada sel yang melawan penyerapan air lebih lanjut.
10. Sel itu ditempatkan dalam labu, yang mana dari perubahan berikut yang terjadi?
Jawaban: Sel buatan akan menjadi bengkak
Alasan: Pada saat sel menyerap air, air tersebut akan masuk ke dalam sel. Namun sel ini tidak akan menyerap air seluruhnya. Dinding yang lentur ini hanya bisa mengembang sampai pada ukuran tertentu saja, dinding ini kemudian akan kaku dan akan melawan penyerapan air lebih lanjut. Pada saat ini sel tersebut membengkak (sangat kaku), yang merupakan keadaan sehat untuk sebagian besar sel tumbuhan.
NIM : 107016300991
Prodi : Fisika
Semester : III (Tiga)
Jawaban Quis II
Biologi Dasar I
1. Dalam hal apakah berbagai macam membran sel eukariotik berbeda?
Jawaban: B. Protein bersifat unik untuk setiap membran.
Alasan : Protein merupakan bahan penyusun utama membran. Para Saintis telah menemukan bahwa membran ternyata tersusun atas lipid dan protein.
Protein membran memiliki daerah hidrofobik dan hidrofilik. Protein ini amfibatik, seperti pasangan fosfolipidnya dalam membran. Jika protein melapisi permukaan membran, bagian-bagian hidrofibiknya akan berada dalam lingkungan equeos.
Pada tahun 1972, S.J. Singer dan G. Nicolson juga menganjurkan macam-macam model suatu membran karena adanya protein pada suatu lokasi yang sesuai dengan karakter amfipatiknya.
Selain itu juga terdapat populasi utama protein membran. Protein integral, umumnya merupakan protein transmembran dan protein porferal, merupakan protein yang secara longgar terikat pada permukaan membran. Dan protein itu sendiri dapat berpindah secara acak di dalam membran.
2. Menurut model mozaik fluida struktur membran, protein membran sebagian besar...
Jawaban: C. Tertanam dalam bilayer lipid
Alasan : Karena membran merupakan klokase banyak protein berbeda-beda yang tertanam dalam matrik fluida bilayer lipid, bilayer fosfolip merupakan penyusun utama membran. Bilayer fosfolipid diantara dua lapisan protein glabular (terbentuk seperti bola). Bilayer ini merupakan fluida penyusun utama membran tersebut, tetapi protein menentukan sebagian besar fungsi spesifik membran.
3. Yang mana dan faktor apa berikut yang cenderung meningkatkan fluiditas membran?
Jawaban: A. Proposisi fosfolipid tak jenuh yang semakin besar.
Alasan : Karena ekor hidro membran tak jenuh fosfolipid memiliki lekukan atau kekusutan yang menghalangi molekul tersusun rapat sehingga meningkatkan fluiditas membran.
Membran tetap berwujud fluida pada suhu lebih rendah jika membran itu banyak mengandung fosfolipid dengan ekor hidrokarbon tak jenuh. Karena ada kekusutan di tempat ikatan gandanya, hidrokarbon tak jenuh tersusun serapat hidrokarbon jenuh.
4. Yang mana dari proses berikut yang mencakup semua yang lain dalam daftar berikut?
Jawaban: D. Transpor pasif
Alasan : Karena transpor pasif merupakan difusi melintas suatu membran. Suatu zat akan berdifusi dari suatu tempat yang lain yang lebih pekat ke tempat yang kurang pekat. Jika suatu membran permeabel terhadap warna, misalkan suatu membran yang memisahkan air murni dari larutan zat pewarna dalam air. Setiap pewarna akan berbaur secara acak, dan tetap bergerak. Mebran itu permeabel selektif sehingga mempengaruhi laju difusi berbagai malekul.
5. Didasarkan pada model penyerapan sukrosa pada gambar 8.17 yang mana dari percobaan berikut yang akan meningkatkan laju transpor sukrosa ke dalam sel?
Jawaban: B. Penurunan pH ekstraseluler.
Alasan : Karena transpor sukrosa yang masuk ke dalam sel dan satu protein dikembalikannya ion hidrogen dengan transpor tersebut. Protein ini dapat mentranslokasikan sukrosa ke dalam sel melawan gradien konsentrasi tetapi hanya jika molekul sukrosanya berpindah bersamaan dengan ion hodrogen yang menggunakan protein transpor sekutu sebagai jalan untuk berdifusi menuruni gradien konsentrasi yang dipertahankan oleh pompa proton.
Pertanyaan no 6 s.d 10
Sel buatan yang terdiri atas larutan equeos yang dibatasi mebran permeabel selektif dicelupkan ke dalam suatu labu yang berisi larutan yang berbeda. Membran ini permeabel terhadap air dan gula sederhana glukosa serta fruktosa tetapi sama sekali tidak permeabel terhadap sukrosa disakarida
Lingkungan
Sel
0,03 M sukrosa 0,01 M sukrosa
0,02 M glukosa 0,01 M glukosa
0,01 M fruktosa
6. Larutan mana yang akan memperlihatkan selisih difusi ke luar sel?
Jawaba: Fruktosa
Alasan : Frustosa ini diibaratkan sebagai lingkungan. Sel itu akan menyerap fruktosa yang ada dalam lingkungan dan masuk ke dalam sel. Dinding kaku yang ada di sel akan membantu penyerapan sukrosa.
7. Larutan mana yang akan memperlihatkan selisih difusi ke luar sel?
Jawaban: Glukosa
Alasan : Glukosa ini akan membantu menyeimbangkan sel terhadap lingkungan.
8. Larutan mana yang akan memperlihatkan selisih difusi ke dalam sel?
Jawaban: Kandungan sel
Alasan : Jika suatu sel dicelupkan dalam lingkungan yang isotonik terhadap sel tersebut, tidak akan ada selisih perpindahan air melintasi membran tersebut. Air melintasi membran, tetapi pada laju sama pada kedua arah. Jika sel tersebut dipindahkan ke dalam larutan hipertonik terhadap sel tersebut. Sel ini akan kehilangkan air yang berpindah ke dalam ke lingkungan, mengkerut dan mungkin saja mati.
Jika kita menempatkan sel tersebut ke dalam larutan yang hipotonik terdapat sel itu, air akan masuk lebih cepat daripada yang meninggalkannya.
9. Ke arah mana akan terjadi selisih perpindahan osmotik air?
Jawaban: Ke dalam
Alasan : Apabila sel berada dalam larutan hipotinik (misalkan direndam dalam air), akan membantu mempertahankan keseimbangan air sel tersebut. Sel ini kemudian akan membengkak hanya sampai pada ukuran tertentu sebelum dinding ini mengarahkan tekanan balik pada sel yang melawan penyerapan air lebih lanjut.
10. Sel itu ditempatkan dalam labu, yang mana dari perubahan berikut yang terjadi?
Jawaban: Sel buatan akan menjadi bengkak
Alasan: Pada saat sel menyerap air, air tersebut akan masuk ke dalam sel. Namun sel ini tidak akan menyerap air seluruhnya. Dinding yang lentur ini hanya bisa mengembang sampai pada ukuran tertentu saja, dinding ini kemudian akan kaku dan akan melawan penyerapan air lebih lanjut. Pada saat ini sel tersebut membengkak (sangat kaku), yang merupakan keadaan sehat untuk sebagian besar sel tumbuhan.
MAKALAH FIKIH & USUL FIKIH KEL.9
oleh: ANJAR SARI
Pendidikan FIsika V
UIN SyariF Hidayatullah Jakarta
BAB II
ISI
A. IJTIHAD
1. PENGERTIAN IJTIHAD
Beberapa definisi mengenai ijtihad:
Secara bahasa ijtihad berarti bersungguh-sungguh, bersusah-payah, menggunakan segenap kemampuan.
Ijtihad (Arab: اجتهاد) adalah sebuah usaha yang sungguh-sungguh, yang sebenarnya bisa dilaksanakan oleh siapa saja yang sudah berusaha mencari ilmu untuk memutuskan suatu perkara yang tidak dibahas dalam Al Quran maupun hadis dengan syarat menggunakan akal sehat dan pertimbangan matang.
Menurut kalangan ulama, ijtihad ini khusus digunakan dalam pengertian usaha yang sungguh-sungguh dari seorang ahli hukum (fuqoha) untuk mengetahui hukum syari’at
Menurut Imam Al-Ghazali mengatakan bahwa ijtihad adalah usaha sungguh-sungguh dari seorang Mujtahid dalam upaya mengetahui atau menetapkan hukum syari’at.
Dari beberapa definisi di atas dapat disimpulakan bahwa ijtihad adalah usaha seseorang dengan sungguh-sungguh menggunakan segenap kemampuan untuk mengetahui atau menetapkan hukum syari’at (memutuskan suatu perkara yang tidak terdapat dalam Al Quran maupun hadis dengan syarat menggunakan akal sehat dan pertimbangan matang).
2. FUNGSI IJTIHAD
Tidak semua hal dalam kehidupan manusia diatur dalam Al-Qur’an dan Al-Hadis secara lengkap. Kondisi awal saat pertama kali diturunkan berbeda dengan kondisi saat sekarang yang sudah modern. Akibarnya permasalahan yang baru selalu berkembang dan diperlukan aturan-aturan baru dalam melaksanakan Ajaran Islam dalam kehidupan sehari-hari.
Jika terjadi persoalan baru bagi kalangan umat Islam di suatu tempat tertentu atau di suatu masa waktu tertentu maka persoalan tersebut dikaji apakah perkara yang dipersoalkan itu sudah ada dan jelas ketentuannya dalam Al Quran atau Al Hadist. Jika sudah ada maka persoalan tersebut harus mengikuti ketentuan yang ada sebagaimana disebutkan dalam Al Quran atau Al Hadits itu. Namun jika persoalan tersebut merupakan perkara yang tidak jelas atau tidak ada ketentuannya dalam Al Quran dan Al Hadist, pada saat itulah maka umat Islam memerlukan ketetapan Ijtihad. Tapi yang berhak membuat Ijtihad adalah mereka yang mengerti dan paham Al Quran dan Al Hadist.
3. JENIS-JENIS IJTIHAD
Dalam melaksanakan ijtihad, para ulama telah membuat metode-metode antara lain sebagai berikut:
(a) Ijma' (ijtihad kolektif)
Yaitu kesepakatan, yakni kesepakatan para ulama dalam menetapkan suatu hukum-hukum dalam agama berdasarkan Al-Qur'an dan Hadits dalam suatu masalah yang terjadi. Setelah para ulama yang berunding, maka didapat keputusan bersama dengan cara ijtihad yang akan disepakati disepakati. Hasil dari ijma adalah fatwa, yaitu keputusan bersama para ulama dan ahli agama yang berwenang untuk diikuti seluruh umat.
(b) Qiyâs (reasoning by analogy)
Yaitu menggabungkan atau menyamakan, artinya menetapkan suatu hukum suatu perkara yang baru yang belum ada pada masa sebelumnya namun memiliki kesamaan dalam sebab, manfaat, bahaya dan berbagai aspek dengan perkara terdahulu sehingga dihukumi sama. Dalam Islam, Ijma dan Qiyas sifatnya darurat, bila memang terdapat hal hal yang ternyata belum ditetapkan pada masa-masa sebelumnya.
(c) Istihsan (preference)
Yaitu menetapkan sesuatu hukum terhadap sesuatu persoalan ijtihadiyah atas dasar prinsip-prinsip umum ajaran Islam seperti keadilan, kasih sayang dan lain-lain. Oleh para ulama istihsan disebut sebagai Qiyas Khofi (analogi samar-samar) atau disebut sebagai pengalihan hukum yang diperoleh dengan Qiyas kepada hukum lain atas pertimbangan kemaslahatan umum. Apabila kita dihadapkan dengan keharusan memilih salah satu diantara dua persoalan yang sama-sama jelek maka kita harus mengambil yang lebih ringan kejelekannya. Dasar istihsan antara lain surat az-Sumar 18.
(d) Mashalihul Mursalah (utility)
Yaitu menetapkan hukum terhadap sesuatu persoalan ijtihadiyah atas pertimbangan kegunaan dan kemanfaatan yang sesuai dengan tujuan syari'at. Perbedaan antara istihsan dan mashalihul mursalah ialah: istihsan mempertimbangkan dasar kemaslahan (kebaikan) itu dengan disertai dalil al-Qur'an/al-Hadits yang umum, sedang mashalihul mursalah mempertimbangkan dasar kepentingan dan kegunaan dengan tanpa adanya dalil yang secara tertulis exsplisit dalam al-Qur'an / al-Hadits.
Beberapa definisi qiyâs (analogi)
1) Menyimpulkan hukum dari yang asal menuju kepada cabangnya, berdasarkan titik persamaan diantara keduanya.
2) Membuktikan hukum definitif untuk yang definitif lainnya, melalui suatu persamaan diantaranya.
3) Tindakan menganalogikan hukum yang sudah ada penjelasan di dalam Al-Qur'an atau Al-Hadis dengan kasus baru yang memiliki persamaan sebab (iladh).
4. KEDUDUKAN IJTIHAD
Berbeda dengan al-Qur'an dan as-Sunnah, ijtihad terikat dengan ketentuan-ketentuan sebagi berikut :
(a) Pada dasarnya yang ditetapkan oleh ijtihad tidak dapat melahirkan keputusan yang mutlak absolut. Sebab ijtihad merupakan aktifitas akal pikiran manusia yang relatif. Sebagai produk pikiran manusia yang relatif maka keputusan daripada suatu ijtihad pun adalah relatif.
(b) Sesuatu keputusan yang ditetapkan oleh ijtihad, mungkin berlaku bagi seseorang tapi tidak berlaku bagi orang lain. Berlaku untuk satu masa / tempat tapi tidak berlaku pada masa / tempat yang lain.
(c) Ijtihad tidak berlaku dalam urusan penambahan ? ibadah mahdhah. Sebab urusan ibadah mahdhah hanya diatur oleh Allah dan Rasulullah.
(d) Keputusan ijtihad tidak boleh bertentangan dengan al-Qur'an dan as-Sunnah.
(e) Dalam proses berijtihad hendaknya dipertimbangkan faktor-faktor motifasi, akibat, kemaslahatan umum, kemanfaatan bersama dan nilai-nilai yang menjadi ciri dan jiwa daripada ajaran Islam.
B. MUJTAHID
1. PENGERTIAN MUJTAHID
Mujrahid adalah orang yang melaksanakan ijtihad, yaitu orang yang mengeluarkan hukum berdasarkan pada Kitabullah dan Sunnah Rasul. Mujtahid disebut juga ”hakim”, sebagaimana tercantum dalam hadits Rasul: “Apabila seorang hakim menetapkan hukum dengan jalan ijtihad, kemudian ia benar, maka ia mendapatkan dua pahala. Namun bila ia menetapkan hukum dengan jalan ijtihad, kemudian ia keliru, maka ia mendapatkan satu pahala.”
Mujtahid juga bisa diartikan orang yang berusaha mengetahui atau menetapkan hukum syari’at (memutuskan suatu perkara yang tidak terdapat dalam Al Quran maupun hadis dengan syarat menggunakan akal sehat dan pertimbangan matang).
2. SYARAT MUJTAHID
Tidak semua orang dapat berijtihad begitu saja dan mengeluarkan fatwa. Untuk mencapai derajat Mujtahid, seseorang harus memenuhi syarat-syarat tertentu. Diantara syarat-syarat mujtahid itu adalah:
(a) Menguasai bahasa Arab. Mujtahid haruslah mampu memahami ucapan orang Arab dan kebiasaan-kebiasaan yang berlaku dalam pemakaian bahasa Arab di kalangan mereka. Sehingga ia dapat membedakan antara ucapan yang sharih, zhahir, mujmal, haqiqat, majaz, umum, khusus, muhkam, mutasyabih, muthlaq, muqoyyad, nash, serta mudah atau tidaknya dalam pemahaman.
(b) Mengetahui Nasakh dan Mansukh dalam Al-Qur’an. Maksudnya memiliki ilmu pengetahuan yang luas tentang ayat-ayat al-Qur'an yang berhubungan dengan masalah hukum, dengan pengertian ia mampu membahas ayat-ayat tersebut untuk menggali hukum.
(c) Berilmu pengetahuan yang luas tentang hadits-hadits Rasul yang berhubungan dengan masalah hukum, dengan arti ia sanggup untuk membahas hadits-hadits tersebut untuk menggali hukum.
(d) Mengetahui sejarah para periwayat hadits, supaya ia dapat menilai sesuatu Hadist, apakah Hadits itu dapat diterima ataukah tidak. Sebab untuk menentukan derajad/nilai suatu Hadits sangat tergantung dengan ihwal perawi yang lazim disebut dengan istilah sanad Hadits. Tanpa mengetahui sejarah perawi Hadits, tidak mungkin kita akan melakukan ta'dil tajrih (screening).
(e) Mengerti ijma’ dan ikhtilaf. Mujtahid haruslah mengetahui ijma’ para ulama dan dasar-dasarnya. Dan mujtahid juga harus mengetahui hal-hal ikhtilaf beserta seluk-beluknya.
(f) Mengetahui Qiyas. Mujtahid haruslah mengetahui jalan-jalan qiyas yang benar. Bahkan boleh dikatakan bahwa ijtihad itu adalah Qiyas itu sendiri.
(g) Mengetahui Asrarusysyari`ah (Rahasia-rahasia Tasyrie`) atau mengetahui maksud-maksud hukum.
(h) Mengetahui ilmu logika/mantik agar ia dapat menghasilkan deduksi yang benar dalam menyatakan suatu pertimbangan hukum dan sanggup mempertahankannya.
(i) Menguasai Qawa`idil Fiqhi,yaitu kaidah-kaidah istinbath hukum/ushul fiqh, agar dengan kaidah-kaidah ini ia mampu mengolah dan menganalisa dalil-dalil hukum untuk menghasilkan hukum suatu permasalahan yang akan diketahuinya.
(j) Telah baligh serta mempunyai pemahaman dan penalaran yang benar.
(k) Mempunyai Aqidah dan niat yang benar.
Jika tidak ada satu orang yang mampu menguasai semua ilmu diatas, berarti dalam mengambil/memutuskan perkara harus hadir semua orang dari setiap penguasaannya dari ilmu tersebut, berarti harus terdapat orang yang mengerti segala ayat dan sunnah, harus terdapat orang yang mengerti nasikh mansukh, harus terdapat orang yang mengerti dengan sempurna bahasa Arab, harus terdapat orang yang mengerti Ushul Fiqih dan lainnya.Bukan hanya terdapat dari sekumpulan yang memiliki pendapat dan ilmu yang sama, lalu timbul kata sepakat.
Pendidikan FIsika V
UIN SyariF Hidayatullah Jakarta
BAB II
ISI
A. IJTIHAD
1. PENGERTIAN IJTIHAD
Beberapa definisi mengenai ijtihad:
Secara bahasa ijtihad berarti bersungguh-sungguh, bersusah-payah, menggunakan segenap kemampuan.
Ijtihad (Arab: اجتهاد) adalah sebuah usaha yang sungguh-sungguh, yang sebenarnya bisa dilaksanakan oleh siapa saja yang sudah berusaha mencari ilmu untuk memutuskan suatu perkara yang tidak dibahas dalam Al Quran maupun hadis dengan syarat menggunakan akal sehat dan pertimbangan matang.
Menurut kalangan ulama, ijtihad ini khusus digunakan dalam pengertian usaha yang sungguh-sungguh dari seorang ahli hukum (fuqoha) untuk mengetahui hukum syari’at
Menurut Imam Al-Ghazali mengatakan bahwa ijtihad adalah usaha sungguh-sungguh dari seorang Mujtahid dalam upaya mengetahui atau menetapkan hukum syari’at.
Dari beberapa definisi di atas dapat disimpulakan bahwa ijtihad adalah usaha seseorang dengan sungguh-sungguh menggunakan segenap kemampuan untuk mengetahui atau menetapkan hukum syari’at (memutuskan suatu perkara yang tidak terdapat dalam Al Quran maupun hadis dengan syarat menggunakan akal sehat dan pertimbangan matang).
2. FUNGSI IJTIHAD
Tidak semua hal dalam kehidupan manusia diatur dalam Al-Qur’an dan Al-Hadis secara lengkap. Kondisi awal saat pertama kali diturunkan berbeda dengan kondisi saat sekarang yang sudah modern. Akibarnya permasalahan yang baru selalu berkembang dan diperlukan aturan-aturan baru dalam melaksanakan Ajaran Islam dalam kehidupan sehari-hari.
Jika terjadi persoalan baru bagi kalangan umat Islam di suatu tempat tertentu atau di suatu masa waktu tertentu maka persoalan tersebut dikaji apakah perkara yang dipersoalkan itu sudah ada dan jelas ketentuannya dalam Al Quran atau Al Hadist. Jika sudah ada maka persoalan tersebut harus mengikuti ketentuan yang ada sebagaimana disebutkan dalam Al Quran atau Al Hadits itu. Namun jika persoalan tersebut merupakan perkara yang tidak jelas atau tidak ada ketentuannya dalam Al Quran dan Al Hadist, pada saat itulah maka umat Islam memerlukan ketetapan Ijtihad. Tapi yang berhak membuat Ijtihad adalah mereka yang mengerti dan paham Al Quran dan Al Hadist.
3. JENIS-JENIS IJTIHAD
Dalam melaksanakan ijtihad, para ulama telah membuat metode-metode antara lain sebagai berikut:
(a) Ijma' (ijtihad kolektif)
Yaitu kesepakatan, yakni kesepakatan para ulama dalam menetapkan suatu hukum-hukum dalam agama berdasarkan Al-Qur'an dan Hadits dalam suatu masalah yang terjadi. Setelah para ulama yang berunding, maka didapat keputusan bersama dengan cara ijtihad yang akan disepakati disepakati. Hasil dari ijma adalah fatwa, yaitu keputusan bersama para ulama dan ahli agama yang berwenang untuk diikuti seluruh umat.
(b) Qiyâs (reasoning by analogy)
Yaitu menggabungkan atau menyamakan, artinya menetapkan suatu hukum suatu perkara yang baru yang belum ada pada masa sebelumnya namun memiliki kesamaan dalam sebab, manfaat, bahaya dan berbagai aspek dengan perkara terdahulu sehingga dihukumi sama. Dalam Islam, Ijma dan Qiyas sifatnya darurat, bila memang terdapat hal hal yang ternyata belum ditetapkan pada masa-masa sebelumnya.
(c) Istihsan (preference)
Yaitu menetapkan sesuatu hukum terhadap sesuatu persoalan ijtihadiyah atas dasar prinsip-prinsip umum ajaran Islam seperti keadilan, kasih sayang dan lain-lain. Oleh para ulama istihsan disebut sebagai Qiyas Khofi (analogi samar-samar) atau disebut sebagai pengalihan hukum yang diperoleh dengan Qiyas kepada hukum lain atas pertimbangan kemaslahatan umum. Apabila kita dihadapkan dengan keharusan memilih salah satu diantara dua persoalan yang sama-sama jelek maka kita harus mengambil yang lebih ringan kejelekannya. Dasar istihsan antara lain surat az-Sumar 18.
(d) Mashalihul Mursalah (utility)
Yaitu menetapkan hukum terhadap sesuatu persoalan ijtihadiyah atas pertimbangan kegunaan dan kemanfaatan yang sesuai dengan tujuan syari'at. Perbedaan antara istihsan dan mashalihul mursalah ialah: istihsan mempertimbangkan dasar kemaslahan (kebaikan) itu dengan disertai dalil al-Qur'an/al-Hadits yang umum, sedang mashalihul mursalah mempertimbangkan dasar kepentingan dan kegunaan dengan tanpa adanya dalil yang secara tertulis exsplisit dalam al-Qur'an / al-Hadits.
Beberapa definisi qiyâs (analogi)
1) Menyimpulkan hukum dari yang asal menuju kepada cabangnya, berdasarkan titik persamaan diantara keduanya.
2) Membuktikan hukum definitif untuk yang definitif lainnya, melalui suatu persamaan diantaranya.
3) Tindakan menganalogikan hukum yang sudah ada penjelasan di dalam Al-Qur'an atau Al-Hadis dengan kasus baru yang memiliki persamaan sebab (iladh).
4. KEDUDUKAN IJTIHAD
Berbeda dengan al-Qur'an dan as-Sunnah, ijtihad terikat dengan ketentuan-ketentuan sebagi berikut :
(a) Pada dasarnya yang ditetapkan oleh ijtihad tidak dapat melahirkan keputusan yang mutlak absolut. Sebab ijtihad merupakan aktifitas akal pikiran manusia yang relatif. Sebagai produk pikiran manusia yang relatif maka keputusan daripada suatu ijtihad pun adalah relatif.
(b) Sesuatu keputusan yang ditetapkan oleh ijtihad, mungkin berlaku bagi seseorang tapi tidak berlaku bagi orang lain. Berlaku untuk satu masa / tempat tapi tidak berlaku pada masa / tempat yang lain.
(c) Ijtihad tidak berlaku dalam urusan penambahan ? ibadah mahdhah. Sebab urusan ibadah mahdhah hanya diatur oleh Allah dan Rasulullah.
(d) Keputusan ijtihad tidak boleh bertentangan dengan al-Qur'an dan as-Sunnah.
(e) Dalam proses berijtihad hendaknya dipertimbangkan faktor-faktor motifasi, akibat, kemaslahatan umum, kemanfaatan bersama dan nilai-nilai yang menjadi ciri dan jiwa daripada ajaran Islam.
B. MUJTAHID
1. PENGERTIAN MUJTAHID
Mujrahid adalah orang yang melaksanakan ijtihad, yaitu orang yang mengeluarkan hukum berdasarkan pada Kitabullah dan Sunnah Rasul. Mujtahid disebut juga ”hakim”, sebagaimana tercantum dalam hadits Rasul: “Apabila seorang hakim menetapkan hukum dengan jalan ijtihad, kemudian ia benar, maka ia mendapatkan dua pahala. Namun bila ia menetapkan hukum dengan jalan ijtihad, kemudian ia keliru, maka ia mendapatkan satu pahala.”
Mujtahid juga bisa diartikan orang yang berusaha mengetahui atau menetapkan hukum syari’at (memutuskan suatu perkara yang tidak terdapat dalam Al Quran maupun hadis dengan syarat menggunakan akal sehat dan pertimbangan matang).
2. SYARAT MUJTAHID
Tidak semua orang dapat berijtihad begitu saja dan mengeluarkan fatwa. Untuk mencapai derajat Mujtahid, seseorang harus memenuhi syarat-syarat tertentu. Diantara syarat-syarat mujtahid itu adalah:
(a) Menguasai bahasa Arab. Mujtahid haruslah mampu memahami ucapan orang Arab dan kebiasaan-kebiasaan yang berlaku dalam pemakaian bahasa Arab di kalangan mereka. Sehingga ia dapat membedakan antara ucapan yang sharih, zhahir, mujmal, haqiqat, majaz, umum, khusus, muhkam, mutasyabih, muthlaq, muqoyyad, nash, serta mudah atau tidaknya dalam pemahaman.
(b) Mengetahui Nasakh dan Mansukh dalam Al-Qur’an. Maksudnya memiliki ilmu pengetahuan yang luas tentang ayat-ayat al-Qur'an yang berhubungan dengan masalah hukum, dengan pengertian ia mampu membahas ayat-ayat tersebut untuk menggali hukum.
(c) Berilmu pengetahuan yang luas tentang hadits-hadits Rasul yang berhubungan dengan masalah hukum, dengan arti ia sanggup untuk membahas hadits-hadits tersebut untuk menggali hukum.
(d) Mengetahui sejarah para periwayat hadits, supaya ia dapat menilai sesuatu Hadist, apakah Hadits itu dapat diterima ataukah tidak. Sebab untuk menentukan derajad/nilai suatu Hadits sangat tergantung dengan ihwal perawi yang lazim disebut dengan istilah sanad Hadits. Tanpa mengetahui sejarah perawi Hadits, tidak mungkin kita akan melakukan ta'dil tajrih (screening).
(e) Mengerti ijma’ dan ikhtilaf. Mujtahid haruslah mengetahui ijma’ para ulama dan dasar-dasarnya. Dan mujtahid juga harus mengetahui hal-hal ikhtilaf beserta seluk-beluknya.
(f) Mengetahui Qiyas. Mujtahid haruslah mengetahui jalan-jalan qiyas yang benar. Bahkan boleh dikatakan bahwa ijtihad itu adalah Qiyas itu sendiri.
(g) Mengetahui Asrarusysyari`ah (Rahasia-rahasia Tasyrie`) atau mengetahui maksud-maksud hukum.
(h) Mengetahui ilmu logika/mantik agar ia dapat menghasilkan deduksi yang benar dalam menyatakan suatu pertimbangan hukum dan sanggup mempertahankannya.
(i) Menguasai Qawa`idil Fiqhi,yaitu kaidah-kaidah istinbath hukum/ushul fiqh, agar dengan kaidah-kaidah ini ia mampu mengolah dan menganalisa dalil-dalil hukum untuk menghasilkan hukum suatu permasalahan yang akan diketahuinya.
(j) Telah baligh serta mempunyai pemahaman dan penalaran yang benar.
(k) Mempunyai Aqidah dan niat yang benar.
Jika tidak ada satu orang yang mampu menguasai semua ilmu diatas, berarti dalam mengambil/memutuskan perkara harus hadir semua orang dari setiap penguasaannya dari ilmu tersebut, berarti harus terdapat orang yang mengerti segala ayat dan sunnah, harus terdapat orang yang mengerti nasikh mansukh, harus terdapat orang yang mengerti dengan sempurna bahasa Arab, harus terdapat orang yang mengerti Ushul Fiqih dan lainnya.Bukan hanya terdapat dari sekumpulan yang memiliki pendapat dan ilmu yang sama, lalu timbul kata sepakat.
Minggu, 11 Januari 2009
irmafa gawe
ini lagi pelatihan pemandian mayat, tapi kasian bgt mayatnya, coz mayatnya idup, alias g' mati.
emang ya panitia irmafa jihad di dalan Allah sampe berani jd mayat. salut deh buat panitia....
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