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How can the speed of light change in the medium when we know that it is always equal to $c$? If we say the speed of light is changing in the medium, it will contradict the Einstein's law of special relativity.

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James and Griffiths, Am J Phys 60, 309-313 1992, treat the transmission and reflection of a plane em wave normally incident on a transparent medium. Using a perturbative approach they argue that the incident electric field polarises the medium, the oscillating dipoles associated with this polarisation radiate gives rise to an additional electric field, which in turn gives rise to an additional polarisation ..... the "radiation from many induced molecular dipoles conspires to produce a single wave propagating at the reduced speed".

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  • $\begingroup$ This is the classical physical model; Fresnel's waves, plus the physics of Maxwell's equations. It does not explain (or even use) photons. $\endgroup$ – Peter Diehr Aug 17 '16 at 23:41
  • $\begingroup$ Sorry, yes you are correct, this is the classical model. $\endgroup$ – jim Aug 18 '16 at 8:54
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The mean speed changes, because the photons scatter off the atoms in the medium which makes their path longer. However, the momentary speed is always equal to $c$.

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  • $\begingroup$ When you say scatter would that be like wiggling back and forth between the atoms as it crosses the medium? I have always wondered if the time and a path like that have ever been compared? Is there an experiment somewhere that has been conducted? $\endgroup$ – Bill Alsept Aug 17 '16 at 19:37
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    $\begingroup$ As this answer comes from Photon, it surely is first hand information. $\endgroup$ – Kamil Maciorowski Aug 17 '16 at 19:38
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    $\begingroup$ This is a very misleading model. For example, it suggests that the photons are randomly changing direction as they bounce onto atoms (which would make them quickly forget their original direction), while in reality they propagate in a straight line. It also doesn't explain the case $n < 1$, which has been observed. $\endgroup$ – knzhou Aug 17 '16 at 21:44
  • $\begingroup$ The form of scattering within the media must preserve the optical coherence, or else the image is lost -- and the media is no longer transparent! $\endgroup$ – Peter Diehr Aug 17 '16 at 23:40
  • $\begingroup$ @knzhou: You are totally right, thanks for your comment $\endgroup$ – Photon Aug 18 '16 at 14:41
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Transparent materials (glass, air) transmit images; if the image is distorted or indistinct, we know that the material is altering the coherence of the optical information. That is, what started out at the beginning has not arrived all at the same time. With enough distortion the image is completely lost.

So what is required for a transparent medium to successfully transmit an image? Since light is a physical wave, the transparent medium must preserve the coherence of the phase information of the light. In a typical glass the phase front is slightly slowed while traveling through the glass; this slowing is encoded in the index of refraction, $n = c/v$.

If the material absorbs some frequencies, the material will appear to be colored; a photon that is absorbed (depending on the energy level structure) can be re-emitted, but this will be at (a) a random time later, and (b) in a random direction. No image for this color! There is an exception: stimulated emission, which is the key to building a laser. But this is not how images are transmitted in a passive material.

The process that transmits images can be summed up as Coherent Forward Scattering: Coherent, because otherwise the image integrity is reduced; Forward, because the image is transmitted in this direction, through the material; and Scattering, the remaining available generalized mechanism at the quantum level.

The result is quite like the Huyghen's wavelet model for light transmission: the photons are the waves that are scattered coherently, and because it is coherent, they are able to interfere both constructively and destructively to maintain the coherence of the overall phase front.

enter image description here

The wavefront slows in the medium due to the coherent forward scattering of the photons; this slightly retards the wavefront, even though the photons are still travelling at $c$

It is the interference that slows the phase velocity through through the material; the individual photons continue to "move" at the speed of light, $c$, but the effective motion of the phase front is slowed.

Richard Feynman devotes some time to this in his lectures on QED: The Strange Theory of Light and Matter

Borrowed in part from my answer to Why is everything not transparent?

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