What if there are two paths of least time?

Asked Jan 18 '20 at 18:21

Active Jan 18 '20 at 18:35

Viewed 53 times

I’m reading Fermat’s principle of least time from the Feynman lectures. And the following question popped.

Suppose we have a medium whose the refractive index is a (continuous) function of the position. Then consider two points $A$ and $B$ in the medium.

Question 1: Can the refractive index be such a function of position that we have in fact two paths of “stationary” time (as I read on Wikipedia, it need not be least) form $A$ to $B$? (The time taken need not be the same for both the paths, but these paths make their corresponding times local extrema.)

Question 2: If such a refractive index medium ceases to exist, why so? If not, which path will the light go?

edited Jan 18 '20 at 18:30

Qmechanic

201,751

asked Jan 18 '20 at 18:21

Atom

1,931

Interesting question. Sounds like a degenerate ground state, so my guess would be that both paths have equal probability "highest probability". – twisted manifold Jan 18 '20 at 18:23
Possible duplicates: https://physics.stackexchange.com/q/298013/2451 and links therein. – Qmechanic Jan 18 '20 at 18:32

What if there are two paths of least time?

0 Answers0