I'll give you the same answer that I used on a 4th year bio-physics final many, many years ago. "Who cares?"
Apparently, our Professor did, and I flunked the exam. (I actually did care, but had no idea how to solve the particular question... kinda like now.)
In all seriousness though, I think a good analogy for this would be to compare the light waves to a slinky. As the slinky comes up against a more dense medium, the "coils" that follow will jamb up, then spread out again once the medium changes again. If the slow-down approaches "stopped", the light will reflect, refract, or even change to heat...