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Speed of light in a medium

  1. May 28, 2008 #1
    I'm a materials engineering junior-to-be(yay summer), and like most material scientists i just kind of assume things I dont really understand when it comes to physics =P But I was pondering about refractive indexes today and...

    Well, WHY does light slow down in a medium? The refractive index of glasses varies with the polorizability of the ions or their electron density so this leads me to believe that that somehow the light interacts with the electrons. I don't know how it would classically interact with the electrons without transfusing energy to them (light doesn't lose energy as it transmits through materials, so it would obviously not) so i was thinking quantum mechanically - which I know almost zippo about (next to the basics they teach you in like, chem in high school. None of that superpositions of states or anything). I know the light interacts with the medium when the energy states match (absorption due to phonons, transitions of electrons to higher orbitals, etc.) but when it doesn't do that - why does it slow down/bend?


    Also, i find myself taking things that i always took for fact and now i don't see how they work:

    How in the world does an electromagnetic wave - an electric field and a magnetic field flying through space - NOT effect a charged particle(electron/proton) classically? Obviously it doesn't but why not? If I shove any other kind of magnetic field next to an electron it reacts, any kind of electric field an electron gets entangled with they react - why not EM waves? Quantum states don't match? But why can't it just give the electron kinetic energy - have an light wave fly near an electron and then the electron speeds off away from the light? But if the mag/elec fields are oscillating pos-neg-pos-neg-pos why doesn't the electron oscillate with it; attract-repel-attract-repel-attract? That would obviously transfer energy, but we don't see degradation of light energy in such a manner so why doesn't it happen?

    >.> <.<, I'll stop rambling now.

    There are probably really simple explanations to these and I'm just overlooking them as usual =P

    Help? - that is if you can understand my babble.
  2. jcsd
  3. May 28, 2008 #2


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    Start by reading post #4 in our FAQ
  4. May 28, 2008 #3
    Already did. It actually isn't that helpful.

    At the end of the post:
    "So the lattice does not absorb this photon [due to phonons] and [instead] it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its
    way through the material and this accumulate the delay."

    But earlier:
    "A common explanation that has been provided is that a photon moving through the material still moves at the speed of c, but when it encounters the atom of the material, it is absorbed by the atom via an atomic transition. After a very slight delay, a photon is then re-emitted. This explanation is incorrect and inconsistent with empirical observations."

    So if I'm correct in reading those - it pretty much contradicts itself right there =P

    It was my knowledge that photons will only interact with a material if it matches the energy of a transition within that material - transferring the energy to a phonon, transferring the energy so a electron gets into a higher orbital, or maybe ejecting an electron. But when light doesn't match any of these energies it doesn't get absorbed - yet it still slows down+bends.

    What kind of interaction with the electrons does it actually have?
  5. May 29, 2008 #4
    The "inconsistency" there is that the common explanation is that the absorption is atomic, and the explanation that follows it is saying that the absorption is a collective effect of the lattice. So there's not really an inconsistency there.

    The main problem I have always had with the absorption-reemission explanations is most of them don't seem to address (1) why the light is reemitted in the same direction it was absorbed in and (2) why polarized light passes through a (non-polarizing) medium without changing its polarization. I think a rigorous second-quantized theoretical description would address these things, which I'd like to see but I am not aware of one (not that I've been searching...) I suspect it's really quite difficult to get out the quantities that one wants to see (time delay of the photon, index of refraction based on microscopic properties, etc.)

    The second explanation here: http://www.madsci.org/posts/archives/may98/893732585.Ph.r.html
    is fairly interesting. It describes the photon passing through the medium as interacting with local virtual states, which is fairly similar to the description provided in the faq, although it seems to ignore any collective behavior of particles in the medium.
  6. May 29, 2008 #5


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    Then you didn't understand what it is trying to say.

    It is saying the ATOMS do not do the absorption. It is the LATTICE VIBRATION mode that is responsible for doing that. That is why optical transmission is different in solids when compared to gasses.

  7. May 29, 2008 #6


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    You need to remember that, as stated in that FAQ, it is meant as a naive explanation for a question most often asked by someone who isn't well-versed in physics, much less, solid state/condensed matter physics. That's why only a cursory explanation is given.

    The preservation of the direction actually is quite well-explained in such transport scenario. It is the same explanation that one gets regarding the interaction of conduction band electrons in preserving the direction of the in-plane momentum of light when it is being reflected off the surface. The phonon modes have a dispersion, which means that it has well-defined "k" (momentum) distribution, similar to the dispersion of the electronic conduction band. So a photon that excites a particular mode in a particular momentum, and via conservation law, that's the mode that will be remitted. So the photon essentially "selects" which mode it is exciting or interacting. That would also explain why, in an unpolarized material, the polarization can still be preserved if the material has an amorphous structure and the modes are not absorbed in any particular direction of the E-field of the photon.

    Including all this in the FAQ would have made it unbearably confusing and unnecessary for what it was trying to answer.

  8. May 29, 2008 #7
    That depends on the wavelength of the light right?. Individual atom's electrons(well, if were talking about ions...i work with ceramics so i usually assume this xD) will absorb UV light, the UV light matches atomic transitions(s1 to p3 or w/e, the exact transition depend son the atom, cordination number, EM energy, etc.) - thats why glasses dont transmit UV or only transmit a certain length into the UV spectra. Phonons will absorb EM waves from the IR spectra as their energies match as well(BTW the transmittance into the IR band is also 'tunable' in glasses just like the UV band, which I thought was interesting). And if you start getting into higher energies they start knocking off electrons, a.k.a. photoelectric effect. Oh, and different atoms absorb different wavelengths obviously - Cu(II) makes glasses blue b/c it absorbs bands of the visible spectra - same wiit other transition metal ions and rare earth ions(due to the 3d and 4f electrons which have transition energies equal to the visible spectra's EM energy). You can also change this with cordination number and oxidation state - but thats getting into ligand field theory =P OH. And if you want to get really cool - you can absorb even DIFFERENT wavelengths if you form nanoparticles in your glass. Like if you want to absorb blue light(and make red glass) you have to control the partial pressure of oxygen in your furnace so you turn Cu(II)(gold is easier to do it with, which is what thhey use to use in the old days in venice) and reduce it to Cu metal - then it forms nanoparticles in your glass which can form standing waves on its surface which - if you make the right size particles - abosrbs blue light and makes you some cool red glass - which use to be worth its weight in gold back in rome, using onlly .2wt% gold in the batch ;D thats a money-maker.

    I think i was looking too far into the FAQ =) If thats all it says then I think thats what I did. So pretty much all its saying is that when were talking about transition of energies to electrons the quantum states that are defined can't be defined from individual atoms but instead rely also on the state of the atom's overall coordination. I understand this - thats why Ni(CN=III) and Ni(CN=IV) absorb different wavelengths - has to do with how close different orbitals are to each other in the geometries of their coordination.

    I've never thought of that 2nd one, but the first one has come across my mind before. It was going to be my second post after somebody answered my first question xD I read [i apparently cant post URLs yet, the one you linked to] and it probably would of confused me more if you didn't mention that it did in fact ignore coordination of atoms. I think the only thing that was tripping me up was the fact I thought you guys were saying that the speed of light change had nothing to do with absorption and readmission idea - that photons were NEVER absorbed or interacted when passing through material if they wern't of the correct energy state. It was a well written explanation but i did have some questions:

    1) If the speed of light is due to light being absorbed and readmitted as the link says - are there really that many atomic states to absorb light at different quanta? I know there are TONS of them(K alpha-beta-etc, L alpha-beta-etc. M, etc, when your talking about transitions) but that doesn't seem enough to cover the entire spectra - is it? Or does it have to do with the 'virtual states' he was talking about?(see #2)

    2) These 'virtual states', was he using them as a means to convey atomic transition and readmission? Like if a EM wave hits an electron then it gets promoted then relaxes. Is this 'virtual' state the same as the 'promoted' state? If its more then a nomenclature thing that opens up a whole new world of quanta to me xD That would mean that things can last outside quanta for a short time, but not for a permanent time - right?

    3) This paragraph:
    confused the bajebus out of me. He describes the light as being...partually absorbed for a while? Like - it says the light and electrons interact. But he says it in a way that suggests that the electron is 'vibrating'(if you think classically) with the wave and will only keep the energy if the energy matches a quantum state. This says to me that sometimes when light passes through matter the light interacts with an electron that in fact does not have that quantum state available to it. This means that electrons will take energy from light even though that quantum state is not available and then give it back. This means that for a short time the electron exists outside of a quantum state o_O;; Is that true? I was under the impression that was a non-possibility - only certain energies could be available and no in-betweens for any amount of time?

    o.o;; All i got out of that was 'momentum is conserved...deal with it' xD I haven't gotten into conduction band reflections or K distributions. =P Thats actually next semester i hope. Or 2nd semester senior year if I decide on the physics minor (I want to take solid state physics really bad >.>)
    Last edited: May 29, 2008
  9. May 29, 2008 #8
    Yeah, I guess I wasn't clear; I wasn't trying to criticize that explanation, because it's probably fine for its target audience, but I was trying to respond to the OP who wasn't satisfied with that explanation, and share that he is not the only one who is unsatisfied by the basic explanation.

    I would certainly expect some conservation of (crystal?) momentum to come out of a rigorous derivation, because that's observed experimentally. But my understanding of non-normal mode vibrations is that they tend to be fairly spacial localized, especially at high frequency, so the idea of this kind of localized vibration caused by a photon retaining a definite momentum is difficult for me to swallow. Maybe it's true, but it will take more than a hand-wavy argument to convince me.
  10. May 29, 2008 #9


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    You need to keep in mind the SCOPE of the explanation. It is explaining light transport in solids. If light starts knocking off electrons, then it is no longer light transport in solids.

    Secondly, UV light transport in solids like glass is STILL governed by the collective phenomena of the solid and not by individual atoms. Why? I can rearrange those Si atoms in such a way that this "glass" can now transmit such UV light. Compare the non-UV transmission of ordinary glass versus fused silica or quartz. What's the difference? Certainly not the element making up the material.

    When the arrangement of the atoms/molecules in the material makes a difference in the property of the material, then this is a big clue that the collective effect is more important here than the individual atoms making up that material. That's one of the major point of that FAQ entry, and something that many people still are not aware of. Again, it is why "atomic/molecular physics" is different than "solid state/condensed matter physics".

  11. May 29, 2008 #10
    Yeah, one of the things you get in a crystal is that atomic states get "smeared" out, so you have states from every atom, but combining them in different ways you get new states that are more extended and have different energies from the atomic energy level. When you have tons of atoms, as in a solid, then there are so many different ways to combine them that you get a band of allowed energies, where you basically can find the right combination of atomic wavefunctions that gives any energy in that band you want. These bands can overlap to produce very large ranges of energy where electronic absorption can occur. Commonly there are regions between the bands, "gaps," where no allowed states are. Of particular interest is the gap between occupied and unoccupied states, which determines whether a material is an insulator or metal. Think of that as a preview of solid-state physics, I guess.

    My understanding of what exactly a virtual state is very poor, but I will try to describe it as thus. The crystal environment determines the allowed states for electrons. Along comes a photon, with its electric and magnetic fields, and now the presence of these fields has changed the environment, thus changing (somehow) what energies are allowed. So an electron can maybe jump into a new state, absorbing energy (and thus the photon?) from the electric field. But now the photon is gone, so the environment is back to a situation where the state the electron was in is no longer allowed, so it has to transition back to an allowed state.

    That's the best hand-wavy argument I know of, except maybe with "electron" replaced with "quasi-particle" (meaning a collective excitation of electrons and/or lattice vibrations).
  12. May 29, 2008 #11


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    This is not quite right, because you are mixing different things together.

    The only way I can illustrate this is the simple 1-D chain where you have an alternating + and - charges, representing the crystal lattice of a solid. You'll note that the "electrons" in question here are bound to the positive ions, so they essentially form the bonds that hold the solid together. There are no "free" electrons, and the "transition" from one energy state to another isn't as clear here as in the atomic case. Rather, the "transition" here is made by the collective solid, and here, there isn't any discrete energy state, but rather a continuous band of energy states, much like the electronic conduction band or valence band of a solid.

    A "quasiparticle", at least from the standard definition from the Landau's Fermi Liquid theory, is a many-body excitation of an electron interacting with OTHER electrons. Here, the many-body interactions have been "renormalized" into a one-body system. A corresponding "quasiparticle" for lattice vibration is the phonon, where it represents the collective excitation of the lattice vibration.

  13. May 29, 2008 #12
    Well, but UV light is still absorbed by electron transitions within the atom? The diffrence in UV absorption in arangements of Si has to do with the lattice, yes. But that doesn't mean that the 'lattice' absorbs it. It depends on the electronic structure of the ion and lattice. Like the example i gave before was nickle. In 6 cordination(octahedral ligan field) the dx^2 and d(x^2-y^2) oribitals have greater energies than the dxy, dxz, and dyz orbitals due them being diffrent distances from the electron fields of the cordination atoms' orbitals. That is diffrent then say in a tetrahedral ligand field - greater overlap of the dxy, dxz, or dyz orbitals with the ligand orbitals have greater energies than the dx^2 and d(x^2-y^2) orbital. This is what your talking of when you say the lattice effects the transitions - as your right in saying. But the transitions are still done within those orbitals. The light is still absorbed due to an atomic change - the electron is going from say the eg orbital to the t2g orbital. Yes, the energies change when you rearange the atoms but the actual transitions are still promotion of electrons through orbitals, even non-hybridized/non-bonded orbitals - which would make them atomic, no?

    If i'm completely wrong correct me, as I'd rather be made a fool of and then smarter for for it then just continue to be wrong =P


    Just read your last post, which probably explains my confusion. You say transitions are made by a collective solid. But for a case in which 1 photon would go through and get absorbed then you would have one electron that would interact with it, correct? I guess i cant make the leap from that to 'made by the collective solid" o_O
    Last edited: May 29, 2008
  14. May 29, 2008 #13


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    I don't know how many times I have to say that this has nothing to do with atomic absorption. Since saying it one more time may not make a difference, I'll stop here, because I have no idea what else to do.

  15. May 29, 2008 #14
    In a solid, orbitals that can accept low-energy excitiations (< 20 or so eV) will always hybridize some with neighboring atoms. Actually, these hybridizations can extend quite far beyond just the first neighbors and it is not atypical to have significant hybridization with a second nearest neighbor.

    Nickel and other transition metals in a solid are often talked about as having d-bands. For the right symmetry, you will often see people talk about t2g and eg bands, instead of orbitals. If you want to talk about atomic states in a solid, you run into one of two problems: 1) they are not orthogonal, so you cannot say that if an electron is in a (e.g.) dxy orbital on one atom you cannot say that it is not also in a dxy orbital on a neighbor, or 2) you construct an orthogonal representation of states (such as Wannier functions or orbitals) and they end up being atomic-like but not atomic. Wannier functions will contain hybridization from other atoms. Either way, there is no way to avoid the idea of an atomic state being hybridized in a solid.
  16. May 29, 2008 #15
    Ah =) Thanks for the explination. I knew about hybridization but never that it went to such an extent. We've never talked about it in detail in any classes either. Hybridization to a 2nd neighbor is really interesting - I didn't think that would happen.

    So, when were talking about absorving UV light the lattice does absorb it, as the orbitals smear out to form the electric structure of the lattice(due to hybridization). So when ZapperZ is talking about lattice vibrations absorbing EM waves he means not just phonon transitions(resulting in heat) but also that the lattice absorbs waves that correspond to electron transitions within the lattice. When i was talking about electron transitions=atomic transitions i was just wrong because i was under the impression that orbitals stayed to their atoms while instead they hybridize over a large number of atoms. I was still thinking with the 100% ionic thing, charged balls and the like =P While if you think about it as not 100% ionic(which stuff rarely is) then you get transitions of the hybridization bonding.

    I like how this turned into a fight on absorption instead of actual speed of light in a medium.

    So back on topic? Lol

    2 questions:

    1) Am I right in thinking that the link you posted to was correct in saying light slows down because of absorption+readmission. The absorption and readmission are done because of the virtual state not being an available transition in the material - no available quantum state, otherwise it would just be absorbed(converted to heat, scattered, etc.). They readmit in the same direction b/c bascially 'momentum is conserved in the lattice', but i'm sure the proof of that is beyond me at the moment =P.

    2) The absorption+readmission is due to electrons reacting with the E+M fields of the wave, correct? How many electrons at one time does the EM wave interact with? If multiple then how many, what effects the number(wavelength?)?
  17. May 30, 2008 #16
    "Well, WHY does light slow down in a medium? The refractive index of glasses varies with the polarizability of the ions or their electron density so this leads me to believe that that somehow the light interacts with the electrons. I don't know how it would classically interact with the electrons without transfusing energy to them (light doesn't lose energy as it transmits through materials, so it would obviously not)"

    light interacts with electrons in a conductor (it is reflected) without losing energy.
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