Thanks, I feel like I've just experienced Feynman's complaint about his Brazilian students not applying their knowledge of the concept of "index of refraction" to an actual physical object. That is, I didn't think about how the whole idea of the index of refraction of a material is directly derived from the different speed of light in that material.
I'm still confused because I thought I had learned that fiber optical cables work by total internal reflection, in which the light inside is repeatedly reflected by the surface of the fiber. Is this an overly simplistic view for thinking about the path that the light will follow in the fiber?
It is a somewhat simplistic view because light isn't just a particle bouncing off walls, its a wave. What happens is that the fiber creates a 'waveguide'. This will gently curve the wavefront around the fiber.
I barely understand this myself. But the way I imagine this is essentially as a water wave running through a trough.
Lets consider a simple sinusoidal wave originating at one end of the trough. Lets call a wavefront any line across the trough that follows the peak of a wave (really it can be any fixed phase, but peaks are nicer to visualize). What happens to these wavefronts as time goes on? They bend around the corners. Essentially the water just in front of the wavefront is going to be pushed up next, and when this happens has a lot more to do with distance from the current wavefront than whether the actual water particles are bouncing off the wall or not.
My explanation of wavefronts moving forward doesn't quite explain why the wavefront 'rotates' in a curved waveguide. I would guess something about path interference being different on the inside of a corner than the outside. Someone who actually studied this stuff probably knows a lot better.
I'm still confused because I thought I had learned that fiber optical cables work by total internal reflection, in which the light inside is repeatedly reflected by the surface of the fiber. Is this an overly simplistic view for thinking about the path that the light will follow in the fiber?