But why would light "slow down"? | Visualizing Feynman's lecture on the refractive index

I realized recently that I didn't really understand how a prism works. The standard explanation, what you might hear in a high school physics class, for example, goes something like this. When light enters a medium like glass, it slows down in the sense that if you look at the crests of the wave in a vacuum, those crests are traveling at C, the speed of light. But inside the glass, those crests will be traveling a little bit slower.

And the specific ratio between the speed of light in a vacuum and the speed inside a medium like this is called the index of refraction for that medium. The reason we use the word refraction instead of say the index of slowing is that if a beam of light enters this glass at an angle then a consequence of this slowdown is that it bends a little bit or using the lingo it refracts. And the way my high school physics teacher always explained this was to imagine a tank going from some region where it can travel relatively quickly, like concrete, into something slower, like mud. Where if it's coming in at an angle, then as one of its treads hits the slow region first, that tread will be going slower while the other one is faster, causing the whole tank to steer a little bit until that second tread also enters the mud.

Then it continues straight, just traveling a little slower. We'll get back to the actual reason for bending in a bit, but at this point, the high school physics students typically learn a law known as Snail's law, which specifies exactly how much things bend. If you draw a line perpendicular to the boundary between the glass and water, and consider the angle between that perpendicular line and the beam of light, then Snell's law tells us that the sign of this angle divided by the speed of the light is always a constant. So, the slower the light, the lower that angle will be.

And that lets you actually calculate how much things refract. What's going on with a prism then is that the specific amount that light slows down depends a little bit on its frequency. For example, blue light, which has a relatively high frequency, would get slowed down more aggressively than red light, which has a relatively low frequency. Now, ...