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Light slows down while passing through, say, water. After passing through the water, does the light speed back up to the "speed of light"? If so, how and why?

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Classical electromagnetic waves, which is what light is, emerge as a confluence of an enormous number of photons, quantum mechanical entities. Light does change velocity through the medium, the photons do not, they always travel at c.

What happens in materials the build up of light by photons changes, because photons undergo elastic and inelastic scatterings and the built up wave has a smaller velocity than c, while the individual photons still have velocity c, due to these elementary quantum mechanical interactions. This appears in the index of refraction given in the other answer.

When there is no matter intervening the photons and the beam they build up have the same velocity c.

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  • $\begingroup$ something about this explanation of the slowdown of light through a medium seems off - as we can bring a wave packed to a standstill in BEC medium, I don't see how the photons can be said to still be traveling at c. $\endgroup$ – JPattarini Feb 29 '16 at 7:33
  • $\begingroup$ Anna V is referring to coherent forward scattering; the slowing applies to the wavefront, and is due to the interference of the Huyghens wavelets created by the scattering. The process in the BEC condensate is due to resonance effects. $\endgroup$ – Peter Diehr Feb 29 '16 at 8:43
  • $\begingroup$ @JamesPattarini You can think of it grossly as the photons scattering and following a longer path length with velocity c, and scattering back into the direction of light. This takes them more time which interpreted for the wavefront gives a smaller velocity than c. $\endgroup$ – anna v Feb 29 '16 at 9:27
  • $\begingroup$ @annav I'm just having trouble seeing how any amount of scattering could result in "stopped" light, or how the vector of group travel can be preserved in such an explanation, ditto for absorption/re-emission explanation that seems to keep popping up despite being abandoned some time ago (I thought). While frequency could be preserved in absorption/re-emission, there is no guarantee of re-emission along the same vector (momentum conservation is satisfied by the initial absorption dynamics of the atom). $\endgroup$ – JPattarini Feb 29 '16 at 9:33
  • $\begingroup$ @annav I think I found the answer to my confusion at physics.stackexchange.com/questions/153904/… Basically (as with most things in QM) I'm both right and wrong. A fully QM explanation is the only way the momentum and direction of group travel both being conserved makes sense. $\endgroup$ – JPattarini Feb 29 '16 at 9:44
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yes. passed each interface, the new refraction index tells the new celerity (and wavelength change). See here Huygens formulation and graphical derivations.

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Without going into the thick of it: light doesn't really slow down inside a transmissive material, so it doesn't speed up upon exiting either.

What it does is interact with the particles of the material, and it is this interactions that slows the effective time of travel.

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