I have attached a picture of a light ray bouncing off a spherical mirror. I wish to show that the travel time of the ray is minimised for $\theta=0$ or $\theta=\pi$. This can be argued geometrically by showing that side EB is greater than side CB, but I was looking for a more analytic approach, namely finding the travel time in terms of theta and differentiating to find the minimum. My main difficulty is actually finding an explicit expression for side EB in terms of R and $\theta$. Any ideas?
2026-04-13 12:01:41.1776081701
How to minimise light propagation time in a spherical mirror?
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