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.

Possible duplicate: How does Fermat's principle make light choose a straight path over a short path? — Qmechanic, Oct 11 '20 at 17:34
Something I find helpful: in this case sound and light have similar behaviors because they are both dominated by wave effects. The SOFAR channel is a region of the ocean where these bending effects actually trap the sound waves. If you understand the sound wave effects here (which are always more intuitive than light effects), its easier to apply them to your case with a change in speed of light, like we see in a prism — Cort Ammon, Oct 11 '20 at 17:40

score 3 · Answer 1 · answered Oct 11 '20 at 17:48

3

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.

answered Oct 11 '20 at 17:48

gandalf61

52,505

Are you saying, there is no way the light can go from s to f and back to s, unless we set up something more complicated like this kind of lense? (In my original idea I would just have two bars of materials lying on top of eachother) – Dennis Jaheruddin Oct 13 '20 at 09:56
@DennisJaheruddin Yes, that is what I am saying. If the f layer is homogenous (the same in all places) then the light beam cannot suddenly change direction in f - if it did then it would not be taking the shortest time route from one place in f to another. Within the f layer the light must travel in a straight line. – gandalf61 Oct 13 '20 at 10:38

score 2 · Answer 2 · answered Oct 11 '20 at 21:45

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.

So from this comment I make: If the light was moving in a clear direction like with a laser, it would not curve downwards in my example. What are your thoughts if I had a lightsource that went in all directions (or would the question even make sense?) — Dennis Jaheruddin, Oct 13 '20 at 09:54

Can light take a (faster) detour?

2 Answers2