actually... light only travels precisely at C in a vacuum, any medium will create resistance in the passage of light through it thereby slowing it down. Generally though this reduction of speed is minute, not even a tenth of a percent of C, however it is possible to significantly reduce the speed of light through various means, even stopping it completely. As is obvious in the natural application of the black hole, but this has been reproduced by man with... less extreme measures.
Didn't that mean that it is actually being constantly absorbed and re-emitted by the medium? Also, I didn't check the specs on those experiments, but I would think that there would be considerable loss of efficiency using a medium due to diffusion and emitted light being more dispersed than in vacuum. Looking into it this seems to be the case. Also if I got it right the light's properties may be changed in the process. So, technically photons are still moving at c but they're constantly bumping into stuff, absorbed, randomly emitted and so on and the medium has been specifically designed so that the dispersion etc., creating a 'maze' that will statistically hold back the light for a period of time.
I'm not exactly an electromagnetic physicist and wiki is hardly the best reference for scientific accuracy so I'm simply going to admit I don't know enough to answer the question adequately, for me the differences between one and the other are irrelevant, and it seems rather unlikely that shall change in the near future. Though this does seem to fit the rules for waves passing through an object...
Oh hey, this thread is pretty cool! I'm taking Modern Physics in college right now. We just finished up Heisenberg's uncertainty principle and started working on the Schrodinger equation right before spring break this week. Most of the info here is spot in from what I've learned! A lot of the mind-bending stuff from relativity (time dilation, length contraction, velocity addition, relativistic doppler effect) all occur because if they didn't, the Standard Model (in terms of relativity, that something with mass would require infinite energy to increase velocity as it approaches the speed of light) would break. As for light moving through a medium, basically consider λν = c, where c is constant, and the frequency is constant (as sheep said, the frequency of light in = frequency of light out), lambda represents the wavelength of light. Thus, the wavelength of light is inversely proportional to the velocity. As we know, the permittivity of a medium with a refractive index greater than 1 will decrease the speed (v) of the light, which increases the wavelength so that c remains constant through a medium. Does that help? This is one of those cool cases where the duality of photons, being particles as well as waves, comes into play. It may slow down the wave packet, but the wave packet's wavelength increases proportionally.
I envy you for having the chance to study the mathematics of it all. There can be no true understanding of physics without understanding the mathematics for it is mathematics that describe to us things that defy intuition and which are otherwise impossible to explain. The abstractions and analogues usually fail to grasp the true nature of the phenomena they describe, they're like the shadows from Allegory of the Cave, whereas mathematics behind a theory is what casts those shadows. I personally think that physics is so fundamentally important for us at explaining the very nature of our existence that is should be taught more widely for everyone. Especially in democratic countries where the power is to rest upon the people it would be of utmost importance to take care of people's education and certain basic level of civilization.
