I'm aware of the classical explanation of refraction which deals with light being a wave that gets "slowed" down while passing from a medium to another. One problem that I have with this explanation is that this explanation cannot apply to a laser beam, which is not a wave in the classical sense.
I found another explanation on this video (minute 6:05) that talks about the light passing by the electrons of the medium and causing them to vibrate, producing an induced light wave. The problem I have with this explanation is that photons are the mediating particle for electromagnetism, so I don't understand how photons can just pass near electrons without being absorbed by them, and causing changes in their momentum at the same time. This sounds like some sort of "action at distance" that requires another mediating particle to be explained.
The same video later (minute 8:39) talks about superposition and how, if we apply the equations of quantum mechanics, we get results that are consistent with the observations. This sounds a lot like a "shut up and calculate" kind of explanation, which is something I can accept, but I'm wondering: is there a more intuitive explanation?