Can light take a (faster) detour?

Question

I was taught that light tends to take the 'fastest' route. However, this made me wonder about the following scenario:

Suppose the start and end point (source and observer) are at the edge of a large cube of one medium,inside it but very close to the edge.

Surrounding the cube is a material through which light can travel much faster.

What would the path look like, would the light go out of the cube and back in again? Would it curve or just have straight turns??

Sketch where the light moves from a-b, in slow material s, close to fast material f, we may assume a and b are quite far from each other:

asssssssssssssssssb
sssssssssssssssssss
fffffffffffffffffff
fffffffffffffffffff

In the real world, the analogy could be seen as: you are in the water close to the coastline, the fastest way here would definitely to leave the water and hop back in near the end, but I am not sure if the analogy makes sense and if light can even do that.

Answer 1

Within a homogenous material, light travels in straight lines. To make light curve as you describe, you would have to vary the refractive index (and hence the effective speed of light) continuously from one side of the cube to the other. What you have then invented is a gradient-index lens.

Answer 2

It is easy to construct situations in which light does not take the "fastest" route. For example, set up a laser pointer to send a beam across the room. Put a mirror in its path and deflect it to a second mirror, then tilt the second mirror to direct the beam to the point on the far wall where the beam would hit if all the mirrors were removed. The "fastest" path is for the beam to just barely dodge around the first mirror, then go to the point on the wall.

So the principle that light takes the "fastest" or "shortest" route should not be taken too literally! The principle does have a useful meaning, but it's actually quite subtle. I personally think it would be better not to teach that as a principle at all.