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We know from fermat's principle that light follows the smallest path. But how light know that which path is smallest?

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Use semiclassical expansion of QED to derive Fermat's principle. Related: physics.stackexchange.com/q/2041/2451 and physics.stackexchange.com/q/29528/2451 –  Qmechanic Mar 31 '13 at 18:50

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A way to understand this, is to imagine that light actually follows all paths. However, most paths experience destructive interference with other paths. The only paths that do not experience destructive interference are those in the neighbourhood of paths with stationary (e.g., minimal) action (time).

I strongly recommend reading Feynman's QED: The Strange Theory of Light and Matter. In the link you'll also find a link to video.

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I would like a mathematical explanation please.. –  T Abraham Jan 17 at 6:48
@TAbraham Perhaps start reading here: en.wikipedia.org/wiki/… –  Glen The Udderboat Jan 17 at 10:42

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