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So light travels slower in glass (for example) than in a vacuum. What causes light to slow down? Or: How does it slow down? If light passes through the medium, is it not essentially traveling in the "vacuum" between the atoms?

Qmechanic
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Henry
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  • Transparency and partial reflection can both be derived with photons interacting with the surfaces only. The speed of light through The medium can be calculated as original speed times the actual distance traveled by the photon as it zigzags through the atoms. The speed as always c – Bill Alsept Dec 27 '16 at 19:37
  • Transparency is zero if medium's width is quite long (Lambert's law).The speed is slowed down even in the air atmosphere. – elias2010 Dec 14 '17 at 08:41

4 Answers4

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The easiest way to get the exact behavior is from thinking about light as a classical wave interacting with the atoms in the solid material. As long as you're far away from any of the resonant frequencies of the relevant atoms, this picture isn't too bad.

You can think each of the atoms as being like a little dipole, consisting of some positive and some negative charge that is driven back and forth by the off-resonant light field. Being an assemblage of charges that are accelerating due to the driving field, these dipoles will radiate, producing waves at the same frequency as the driving field, but slightly out of phase with it (because a dipole being driven at a frequency other than its resonance frequency will be slightly out of phase with the driving field). The total light field in the material will be the sum of the driving light field and the field produced by the oscillating dipoles. If you go through a little bit of math, you find that this gives you a beam in the same direction as the original beam-- the waves going out to the sides will mostly interfere destructively with each other-- with the same frequency but with a slight delay compared to the driving field. This delay registers as a slowing of the speed of the wave passing through the medium. The exact amount of the delay depends on the particulars of the material, such as the exact resonant frequencies of the atoms in question.

As long as you're not too close to one of the resonant frequencies, this gives you a really good approximation of the effect (and "too close" here is a pretty narrow range). It works well enough that most people who deal with this stuff stay with this kind of picture, rather than talking in terms of photons. The basic idea of treating the atoms like little dipoles is a variant of "Huygens's Principle," by the way, which is a general technique for thinking about how waves behave.

Chad Orzel
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    I love the chain of reasoning that this derivation follows. Local minima look like parabolas, driven particles in parabolic potentials shake at the drive frequency with a phase shift, a uniform plane of charge oscillating in-phase radiates only forwards and backwards, and stacked uniform planes oscillating with juuuust the right relative phase radiate only forwards.

    This makes me wonder how an extremely dilute gas would affect optical propagation, as the mean separation of atoms becomes comparable to the wavelength. I wonder if astronomers have to take this into account...

     – Andrew Nov 13 '12 at 13:41
  • So there is a slight delay from atom to atom.Therefore this delay must appears as a slowing of the speed of light INSIDE the medium: But,light speed remains constant inside a medium. – elias2010 May 15 '17 at 08:42
  • Does this mechanism also applies to the air? – elias2010 Dec 14 '17 at 08:29
  • Yes, this applies to air too. Molecules can be regarded as Lorentz oscillators. The field is 90 degrees out of phase. The amplitude is small, so this gives a small phase shift to the total wave. –  Jan 11 '18 at 20:31
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    "If you go through a little bit of math, you find that this gives you a beam in the same direction as the original beam" Can you give the math part? Also when you say "slowing of the speed" do you mean "group speed"? @ChadOrzel – SRS Feb 09 '19 at 17:15
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    Great answer :) I recommend this video by Fermilab, which explains the same idea with nice visuals. – thomasfermi Nov 17 '21 at 12:06
  • Oscillation of the free electrons (i.g. inside a TV antenna) is known. Oscillation of the orbital electrons inside a material is known as the fluorescent effect, having a different result. – elias2010 Jan 24 '22 at 08:36
  • This is maybe a dumb question, but what causes the delay in the field produced by the dipoles? Is it just their non-zero mass, which means they have non-instantaneous acceleration and thus lag behind the original field a bit? – yshavit Apr 10 '22 at 05:34
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Thinking of light as a wave, you can see that when a wave pass through a medium, its wavelength is perturbed a little (in the same way as you would expect a change when a wave is produced in the water and pass through an obstacle). Therefore, given the relation $\lambda = v/f$, it is obvious that the velocity needs to change.

r_31415
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  • lamda= v/f not lamda=v*f – Mockingbird Dec 27 '16 at 05:09
  • Wave turns to a longer wavelength? Does a visible ray change color inside glass? – elias2010 Dec 14 '17 at 08:00
  • @elias2010 The wavelength changes because velocity changes, but its frequency remains the same, so you won't notice a change in color. – r_31415 Dec 14 '17 at 08:50
  • No, color depends on the frequency http://www.tedmontgomery.com/bblovrvw/emails/lightfrequency.html – r_31415 Dec 14 '17 at 16:54
  • So,Robert you claim that there is no energy loss during the process?(E=h*f) – elias2010 Dec 15 '17 at 07:44
  • @elias2010 Correct. – r_31415 Dec 16 '17 at 17:29
  • Then,how is the ray finally absorbed?(Beer-Lambert) – elias2010 Dec 25 '17 at 17:37
  • Beer–Lambert law assumes additional phenomena: absorption and scattering. Individual photons can be absorbed or scattered depending on specific properties of the material and frequency of photons passing through such material and that's when the radiant flux changes. In other instances, photons interact with the material without losing energy in the process. – r_31415 Dec 25 '17 at 19:09
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alt text
Here is a nice explanation.

Pratik Deoghare
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    No it is a quantum mechanic effect. Light is an electromagnetic radiation, the combined electromagnetic radiation of photon and electron produces a net wave which is slower Quantum super position means multiple paths thus larger distance but it does not mean it bends in different paths in classical sense, it just super imposes

    https://youtu.be/CiHN0ZWE5bk and https://youtu.be/YW8KuMtVpug is good explanation

    Light phase speed and group speed is different, phase speed can be even faster in some cases https://goo.gl/FdrF3K

     – zainengineer Apr 13 '16 at 12:32
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    @zainengineer You can do a perfectly good job of describing the microscopic source of the index of refraction in classical E&M, and the behavior of driven oscillators if key to such a description (including getting a phase difference). None the less this figure is just awful. – dmckee --- ex-moderator kitten Mar 04 '17 at 20:19
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    This is actually not correct, the light is not absorbed in this way. If it did how will the atom remember in which direction to emit it? So in this case light will just scatter instead of going in straight line. – AVX-42 May 09 '21 at 15:14
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Photons interact with matter all the time when passing through a medium. Only particular frequencies are resonant with the electronic (or rotovibronic) levels in the molecules and get to promote an excitation (thus originating colors, for example), but for most part they are just an electromagnetic disturbance which still has an effect. This interaction slows the propagation of the photon down.

Stefano Borini
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