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Thread: Transparency and Refraction

  1. #1 Transparency and Refraction 
    Senior Member AlexG's Avatar
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    This is a video of Prof Phil Moriarity explaining why glass was transparent.

    Why is glass transparent? - YouTube

    His explanation was basically that the arrangement of the atoms, and consequently the electrons, was such that the energy needed to raise the electrons to the next available energy level was more than photons of visible light possessed. Consequently, the photons could not interact with those electrons and so passed through the glass unchanged.

    While this makes sense to me, it does raise a question in my mind. If the photons do not interact with the electrons and simply pass through the material, what causes refraction?
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    Quote Originally Posted by AlexG View Post
    This is a video of Prof Phil Moriarity explaining why glass was transparent.

    Why is glass transparent? - YouTube

    His explanation was basically that the arrangement of the atoms, and consequently the electrons, was such that the energy needed to raise the electrons to the next available energy level was more than photons of visible light possessed. Consequently, the photons could not interact with those electrons and so passed through the glass unchanged.

    While this makes sense to me, it does raise a question in my mind. If the photons do not interact with the electrons and simply pass through the material, what causes refraction?
    This is a very good question, AlexG, and in fact I don't really know the answer for certain. My thinking is that it probably has to do with scattering. While transparency is caused by the fact that these photons don't have enough energy to raise the outer electrons to a higher energy level ( and thus pass through unhindered ), that does not mean that they don't interact with the atoms making up the material. In fact they do - they get scattered on those same atoms, even if they don't get absorbed. What this means is the photons don't move along straight lines in the material, but rather along some zig-zag trajectory, meaning they take longer to cross the material than they would for the same distance in vacuum. In other words - within the material the apparent speed of propagation is lower, and thus you have a refractive index which differs from 1.
    Not sure though if this is the right explanation - perhaps someone with deeper knowledge of optics can comment.
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    That has bothered me a lot, just like simple reflection has bothered me a lot. Feynman being my personal God, this somewhat semi classical explanation has answered most of it.
    Probably because I can process better an electromagnetic field, that its "quantization", that is the photon.
    Altough I have no clue how the math can compute the result of the radiation and the multitude of re-radiation, based on the material geometry (of the electron cloud). But nature can, and it is quite beautiful, sometimes...
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    Quote Originally Posted by AlexG View Post

    While this makes sense to me, it does raise a question in my mind. If the photons do not interact with the electrons and simply pass through the material, what causes refraction?
    That is mathematically one of the most annoying things I ever had to calculate.

    First of; refraction in materials occurs because the speed of light is different in different materials. Since the energy (frequency) of the wave cannot change, it changes its wavelength and or its speed.

    The speed of a light in a material is a property which is determined by its electric susceptibility and its magnetic permeability.

    So if these change from their values of vacuum, then the speed of light changes. (take not that waves have a phase speed, and a group speed, and that information is never transmitted faster then light, though waves can travel faster then light is certain media.)

    The electric susceptibility changes because the electric field of the light wave changes how electrons in the material react, these on their turn change how the electric surrounding is affected of the medium, changing in its turn the electric susceptibility and therefore changing the speed of light inside the material.
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    Quote Originally Posted by Kerling View Post
    The electric susceptibility changes because the electric field of the light wave changes how electrons in the material react, these on their turn change how the electric surrounding is affected of the medium, changing in its turn the electric susceptibility and therefore changing the speed of light inside the material.
    Hm. This leaves me scratching my head a little bit; why would the presence of electric and magnetic fields change the permittivity and permeability of the vacuum between the atoms making up the material ?
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    Quote Originally Posted by Markus Hanke View Post
    Hm. This leaves me scratching my head a little bit; why would the presence of electric and magnetic fields change the permittivity and permeability of the vacuum between the atoms making up the material ?
    Well, I attributed the permeability/permittivity(p/p) to the geometry and other property (like energy level) of various electron "clouds". Isn't ther, in a solid/liquid, NO actual vacuum between those clouds, suppose to be bounded together ? Anyway your reflection (lol) hold for gases, where I though the vacuum would actually be the main componant of those number(p/p). But they are still measurable, and big, so there is not so much vacuums either in gazes (for an electro/magnetic field anyway :-)
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    Quote Originally Posted by Boing3000 View Post
    Well, I attributed the permeability/permittivity(p/p) to the geometry and other property (like energy level) of various electron "clouds". Isn't ther, in a solid/liquid, NO actual vacuum between those clouds, suppose to be bounded together ? Anyway your reflection (lol) hold for gases, where I though the vacuum would actually be the main componant of those number(p/p). But they are still measurable, and big, so there is not so much vacuums either in gazes (for an electro/magnetic field anyway :-)
    Ok, I get what you are trying to say. My doubts remain, however - I agree that the probability functions for the electrons are not zero between the atoms in the lattice, but once we go beyond - say - the Bohr radius of the atom the probability density becomes so small as to be almost zero. Question is - is that enough to account for the differences in permittivity and permeability ?
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    Quote Originally Posted by AlexG View Post
    While this makes sense to me, it does raise a question in my mind. If the photons do not interact with the electrons and simply pass through the material, what causes refraction?
    I believe it is to do with energy levels available to electrons.

    I haven't watched the video, but it seems to me that "do not interact" is an exaggeration. They may interact but the photons are not absorbed (by bumping electrons to higher energy levels, because the available energy levels are out of reach) as they would do in an opaque, coloured material.

    At the other extreme, there are metals where the electrons form a "sea" with, effectively, a continuous distribution of electrons. This is what makes most metals reflective (photons of all energies are reflected).

    In between, photons are absorbed or reflected depending on frequency.

    Understanding exactly why particular atoms (and collections of atoms) provide electrons with these energy levels and exactly how the electrons interact with photons in all these materials is somewhat beyond me (despite reading Fyenman's QED ).
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    Quote Originally Posted by Markus Hanke View Post
    Ok, I get what you are trying to say. My doubts remain, however - I agree that the probability functions for the electrons are not zero between the atoms in the lattice, but once we go beyond - say - the Bohr radius of the atom the probability density becomes so small as to be almost zero. Question is - is that enough to account for the differences in permittivity and permeability ?
    I have no idea of that probability, but the Van der Walls radius is only 2-3 times bigger the Bohrs radius. In any actual transparent material like water there is not only simple hydrogen, but atom with more complicated etectron configuration, what I call clouds (do not forget I am the layman here ;-) with various shapes and densities.
    I suppose that measuring this p/p quantity for a "material" imply to use some billition'th of atom/molecule, and that what's left is the average of the 'more or less' vacuums, or cloudy landscape.

    What I cannot understand is when some photon (or more likely e/m field wave) jiggle one atom (instead of boosting one of its cloud), and that he re-emit it afterward in more random manner, is that the whole thing keep coherent enough, just like if a photon had pass trough (well deviated, and slowed, but not 'noised'). The speed or delay in this re-emission is also mysterious thins for me.
    Last edited by Boing3000; 01-20-2013 at 03:12 PM.
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    Quote Originally Posted by Markus Hanke View Post
    Hm. This leaves me scratching my head a little bit; why would the presence of electric and magnetic fields change the permittivity and permeability of the vacuum between the atoms making up the material ?
    To be honest, this isn't very easy to do. And quite frankly I took me a lot of time to find out just how it works. It was part of my thesis, and I can honestly say that most optics people don't know how to do it. But it goes as follows:

    First of all, Susceptibility changes, due to a change in electromagnetic behavior of the medium induced by a wave. So how does this come by? Well, first of all, it must be realized that even with an applied electromagnetic field over the atoms, they are still atoms. And they are discrete. This means that a continuous shift isn't possible at all.

    In effect there is a state in which the medium is perturbed by the wave of light, and there is state where it is not. In each state there are seperate different stable states for electrons to have a probability to be in. Hence calculating the probability for the system to change into another state, and using that as a weighing factor to the actual electromagnetic change of the quantum states, gives you the effective electric susceptibility (in most practical cases the magnetic field of light is not strong enough to cause any magnetic changes inside atoms).

    In reality this is a bitch as you need to find transition possibilities for every possible levels. If you'd do it rigorously this means n! terms to calculate the probabilities of, in which n is the amount of possible states... This grows really fast. In reality though it is most often assumed that only the lowest of transitions contribute and this is a good approximation. Making it all a little less cumbersome. But often still, not analytically solvable.
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    Way back in the last century, either toward the end of my formal education or when I was beginning teaching and needed qualitative explanations for phenomena requiring mathematics my classes weren't ready for, I picked up the argument below for light going at a speed less than c in matter. At the time, it seemed to fit the mathematics pretty well. As a caution, however, I don't see how it would work for kappa < 1, where the apparent light velocity is > c.

    It goes like this. As an electromagnetic wave passes through matter, it occasionally kicks an electron in an atom to a higher but temporary state, a resonance. The resonance then decays back directly to the ground state. This process amounts to the temporary absorption of a photon and its re-emission after a delay that is on average the lifetime of the resonance. As a result, the passage of the photon through the material is slightly delayed, so its velocity is reduced. When the photon is actually in existence it is traveling at the speed of light as required by relativity, but the temporary absorptions delay its progress so that its apparent velocity is less. The stimulated emission process of quantum mechanics can be used to argue that the re-emitted photon travels in phase with the original. The usual wave arguments of classical optics then give the correction refraction angle of light going into a substance.

    I still think that this argument has only a reasonable number of over-simplifications and is about as good as any semi-mathematical argument is. It handles absorption fine: if the absorption of the photon knocks the electron off the atom entirely, the light ray will be absorbed. In terms of the original video, if the energy of the photon is enough to kick a bound electron into the solid's conduction band, the light can be absorbed. If not, the unoccupied valence states of the atoms will provide the delay necessary for the permittivity to be greater than one.

    It would be nice if the argument applied to a permittivity less than one also, but I don't immediately see how it would.
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    Well there are metamaterials which have a inner light speed larger then c. However these require complex numbers to understand. And that isn't really an easier argument.
    However the problem of your explanation would be that students might get the idea that light is actually absorbed. I personally think that electronic pressure against the lightbeam is better. As the energy of the light does not increase, and so neither does its power, it slows down when it runs into more troublesome media. Which in effect is somewhat what happens, but then with electronic probabilities.
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    Quote Originally Posted by Kerling View Post
    Well there are metamaterials which have a inner light speed larger then c. However these require complex numbers to understand. And that isn't really an easier argument.
    However the problem of your explanation would be that students might get the idea that light is actually absorbed. I personally think that electronic pressure against the lightbeam is better. As the energy of the light does not increase, and so neither does its power, it slows down when it runs into more troublesome media. Which in effect is somewhat what happens, but then with electronic probabilities.
    Well, as usual it takes more than one qualitative argument to get at all the aspects of the mathematical argument. Personally, I would use mine and emphasize that the photon is not permanently absorbed, and then there is a chance we can get into a discussion of resonance. Also, the photon really is temporarily absorbed; that is why the light is delayed. Usually when this discussion comes up, the student's problem is the conflict with the principle that photons always move at a speed of c, and your argument would leave them with the impression that they really don't. This impression will cause problems when they are studying special relativity.

    Edit: Correct typo
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    when light is reflected it travels at speed c,and carries details of the opaque material,while if light is refracted before transmitted it re-gains its speed c after traveling<c.it sometimes carry details or not.but i will look at it without carrying details.

    the question is,what happens to the information of the material?
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    Quote Originally Posted by mvb View Post
    Well, as usual it takes more than one qualitative argument to get at all the aspects of the mathematical argument. Personally, I would use mine and emphasize that the photon is not permanently absorbed, and then there is a chance we can get into a discussion of resonance. Also, the photon really is temporarily absorbed; that is why the light is delayed. Usually when this discussion comes up, the student's problem is the conflict with the principle that photons always move at a speed of c, and your argument would leave them with the impression that they really don't. This impression will cause problems when they are studying special relativity.

    Edit: Correct typo
    I don't agree. Of course light travels with the speed of light. But it be weird to assume this to be constant. No wave has the same speed everywhere. Why exclude light from this obvious rule? Sound moves quicker through steel then through air for instance. The problem with your explanations is of course apparent for a quick thinking student: Why does the photon get emitted in the same direction as it was absorbed? Let alone arguments like birefringence. Which you cannot explain without using my explanations for different light speeds. Of course the choice is yours. But your explanation is like telling children the stork brings children. And then wonder howcome they have unsafe sex. It is perhaps a little harsh example. But I don't think it will be a very cognitively hard explanation altogether.

    Also for SR, they only need to know, you cannot travel faster then light. not that it is constant.
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    Quote Originally Posted by Kerling View Post
    I don't agree. Of course light travels with the speed of light. But it be weird to assume this to be constant. No wave has the same speed everywhere. Why exclude light from this obvious rule? Sound moves quicker through steel then through air for instance. The problem with your explanations is of course apparent for a quick thinking student: Why does the photon get emitted in the same direction as it was absorbed? Let alone arguments like birefringence. Which you cannot explain without using my explanations for different light speeds. Of course the choice is yours. But your explanation is like telling children the stork brings children. And then wonder howcome they have unsafe sex. It is perhaps a little harsh example. But I don't think it will be a very cognitively hard explanation altogether.

    Also for SR, they only need to know, you cannot travel faster then light. not that it is constant.
    First what I think is the crux of the matter: should the light re-emitted from an atom in a dielectric travel in the same direction as the overall wave? Suppose we have an electromagnetic field travelling past an atom which is in an excited state, and the photons in the passing wave have an energy equal to the energy difference between the atom's ground state and the excited state. This is in fact what we do have when light is passing through a transparent material and one of the photons is absorbed by exciting the atom. In this case, quantum mechanics shows that the passing wave will stimulate the emission of a photon from the excited atom, and the photon goes in the direction of the passing wave and in phase with it. So it is natural, and in fact necessary, that photons will be emitted which continue the light beam. The odd photons that go in another direction provide the partial cloudiness that even the best "traasparent" materials display.

    Now about the constant speed of light. The equations of electromagnetism contain constants which get combined to give the speed of a moving light wave. The equations can be written in any special-relativistic frame and are the same in all of them, and the values of the constants are the same in every frame. Hence the speed of the wave does not change with frame. Since these equations fit an awful lot of data, we are forced to say that the speed of light is the same in any frame. One then needs an explanation why the effective speed of light in a dielectric is less than the vacuum value. The process that I outline is that explanation. The explanation is correct, and the only real question is what is the best description of this process to give to students who don't yet know quantum mechanics. My experience is that the explanation I have outlined works with real students without misleading them about what they will learn in later courses.
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    Quote Originally Posted by mvb View Post
    First what I think is the crux of the matter: should the light re-emitted from an atom in a dielectric travel in the same direction as the overall wave? Suppose we have an electromagnetic field travelling past an atom which is in an excited state, and the photons in the passing wave have an energy equal to the energy difference between the atom's ground state and the excited state. This is in fact what we do have when light is passing through a transparent material and one of the photons is absorbed by exciting the atom. In this case, quantum mechanics shows that the passing wave will stimulate the emission of a photon from the excited atom, and the photon goes in the direction of the passing wave and in phase with it. So it is natural, and in fact necessary, that photons will be emitted which continue the light beam. The odd photons that go in another direction provide the partial cloudiness that even the best "transparent" materials display.
    I was afraid you'd say that. You see, you cannot use stimulated radiation as an argument. First of, because it would require you to have a population inversion. And hence your lens must be pumped in order to be transparant. Which obviously is not the case. Second the resulting broadening of the light would be very different then what is to be expected from normal refraction, and third because it doesn't explain why different colours have different refractive indices.

    And probably more importantly, you'd be required to convince students that it is done by stimulated radiation? Come now, Explaining the speed of light differs is far simpler, and far more true, then some weird absorbtion and stimulated emission story. You might get away with it on some secundary school where the students just don't ask questions. But on a university, maybe even a college. You'd get weird looks from both students, and especially colleagues. If one of my colleagues would give such an explanation, I'd have my serious doubts about his competences as a physicist.

    Now about the constant speed of light. The equations of electromagnetism contain constants which get combined to give the speed of a moving light wave. The equations can be written in any special-relativistic frame and are the same in all of them, and the values of the constants are the same in every frame. Hence the speed of the wave does not change with frame.
    I never stated that, what I state is that the speed of light is different for different media.

    Since these equations fit an awful lot of data, we are forced to say that the speed of light is the same in any frame. One then needs an explanation why the effective speed of light in a dielectric is less than the vacuum value. The process that I outline is that explanation.
    Special relativity is about reference frames. a dielectric is not a different reference frame, but a differen medium.

    The explanation is correct, and the only real question is what is the best description of this process to give to students who don't yet know quantum mechanics. My experience is that the explanation I have outlined works with real students without misleading them about what they will learn in later courses.
    alright how about this one:

    "Light is wave, hence it has different speeds in different propagation media. Just like soundwaves travel with different speeds through air or metal. Or how water waves have different speeds then oil waves. And so it does in for instance glass or an other metal.
    Now, light is an electromagnetic wave. Meaning that perpendicular to its propagation direction there are a magnetic and electric field. Now the magnetic field isn't very strong. But the electric field has some effect upon the material it passes through. If it doesn't become absorbed by the material due to its transparancy. The light still perturbs the medium. A bit like a truck driving fast, you don't need to be hit by the truck to notice that it has past. You'll feel a slight disturbance of air. In this case the electric field of the lights does the same as the truck, but then with the electron clouds inside the medium. Because of this the light changes the transparency parameters of the medium. A bit like a drag behind a racingcar. The medium counteracts the displacement by the light. And slightly breaks the light, slowing it down. However once it leaves the medium this is of course no longer a problem."

    Your explanation misleads them about future optics and condensed matter theory. Also the above explanation doesn't violate special relativity. (because it is what happens) If someone asks the question 'but everything should go with the speed of light'. Then say, but this does, but the speed of light differs. There is good reason why the speed of light 299792458 m/s is defined as the speed of light in vacuum.
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    Quote Originally Posted by Kerling View Post
    I was afraid you'd say that. You see, you cannot use stimulated radiation as an argument. First of, because it would require you to have a population inversion. And hence your lens must be pumped in order to be transparant. Which obviously is not the case.
    Each photon that is absorbed by a resonance produces an excited state that can be de-excited by stimulated readiation. If you had a true, preexisting population inversion, you would get more light coming out than went in.

    It seems clear that we are never going to agree about this. If anyone else is actually interested, they can consult some books to decide which of us to believe. I think it is time we stopped cluttering the forum with this discussion.
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    Quote Originally Posted by mvb View Post
    Each photon that is absorbed by a resonance produces an excited state that can be de-excited by stimulated readiation.
    To quote wikipedia:
    "the process is identical in form to atomic absorption in which the energy of an absorbed photon causes an identical but opposite atomic transition: from the lower level to a higher energy level. In normal media at thermal equilibrium, absorption exceeds stimulated emission because there are more electrons in the lower energy states than in the higher energy states. However, when a population inversion is present the rate of stimulated emission exceeds that of absorption, and a net optical amplification can be achieved."

    To quote from my head, you need at least half of your population to be exited for amplification to occur. And even if you were to pressume that the stimulated radiation was to somehow magically occur, you'd still have spontaneous emission. Which you simply can't turn off. It is a wrong and untrue description is many different ways.
    It seems clear that we are never going to agree about this. If anyone else is actually interested, they can consult some books to decide which of us to believe. I think it is time we stopped cluttering the forum with this discussion.
    In that case I'd recommend 'The Quantum Theory of Light' By Rodney Loudon.
    A good explanantion on stimulated radiation can be found in any good quantum book. One can try quantum mechanics by Bransden & Joachain. Or simply Sakurai.
    A relatively simple derivation of Transparency can be found in chapter 10 of Kittel's Introduction to Solid state physics. (first few pages of the chapter)
    For the more advanced reader; I'd recommend Laser and Elctro-Optics (fundamentals and engineering) by Davis. It has much more on optics.
    To actually calculate the electric optics of any quantum system I refer to Volume 5 of Landau and Lifshitz. It is to my knowledge the only book that makes an explicit reference to attempting to solve this. And it isn't easy, no really I did my thesis about it. But that is so far all I have in the cupboard of my desk.

    Good luck!
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