How does a photon travel through glass? This was discussed in an answer to a related question but I think that it deserves a separate and, hopefully, more clear answer.
Consider a single photon ($\lambda$=532 nm) traveling through a plate of perfect glass with a refractive index $n=1.5$. We know that it does not change its direction or other characteristics in any particular way and propagating 1 cm through such glass is equivalent to 1.5 cm of vacuum. Apparently, the photon interacts with glass, but what is the physical nature of this interaction?
Let's not consider high-order effects like Rayleigh/Raman scattering.
 A: This is a tricky question to answer, because in many ways it doesn't make sense to talk about a definite path followed by a single photon. Quantum mechanics is inherently probabilistic, so all we can really talk about are the probabilities of various outcomes over many repeated experiments with identically prepared initial states. All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other.
The transmission of light through a medium is easier to explain in a classical sense, where you think of the light beam as a wave that drives oscillations in the atomic dipoles making up the material. Each atom then re-radiates its own waves at the same frequency, but slightly out of phase. The sum of the initial wave and the re-radiated wave is a wave that lags behind the incoming wave a little bit, which explains the reduced speed. A beam of light entering a block of material tends to continue in the same direction because forward scattered light from any individual atom tends to interfere constructively with forward scattered light from other atoms in the material, while light scattered off to the sides mostly interferes destructively, and cancels out.
Carrying this picture over to the quantum regime, you would say that a single photon entering the material will potentially be absorbed and re-emitted by each of the atoms making up the first layer of the material. Since we cannot directly measure which atom did the absorbing, though, we treat the situation mathematically as a superposition of all the possible outcomes, namely, each of the atoms absorbing then re-emitting the photon. Then, when we come to the next layer of the material, we first need to add up all the wavefunctions corresponding to all the possible absorptions and re-emissions, and when we do that, we find that just as in the classical wave case, the most likely result is for the photon to continue on in the same direction it was originally headed. Then we repeat the process for all the atoms in the second layer, and the third, and so on.
At any given layer, the probability of being absorbed then re-emitted by any individual atom is pretty tiny, but there are vast numbers of atoms in a typical solid, so the odds are that the photon will be absorbed and re-emitted during the passage through the glass are very good. Thus, on average, the photon will be delayed relative to one that passes through an equal length of vacuum, giving rise to the lower observed transmission velocity. 
Of course, it's not possible to observe the exact path taken by any photon-- that is, which specific atoms it scattered from-- and if we attempted to make such a measurement, it would change the path of the photon to such a degree as to be completely useless. Thus, when we talk about the transmission of a single photon through a refractive material, we assign the photon a velocity that is the average velocity determined from many realizations of the single photon experiment, and go from there.
