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I know in order to compensate with change in speed but how does Light actually know which path is less dense or more dense?

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  • $\begingroup$ I suggest you read 'QED' by Richard Feynman. $\endgroup$ – Physics May 26 at 16:14
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Light doesn't actually 'know' which path is the shortest. In the quantum mechanical description, light actually takes all paths between point A and point B. It turns out that the phase of different paths adds up in such a way that the classical path corresponds to the one in which time taken is the least. For a more detailed explanation read QED: The Strange Theory of Light and Matter by Richard Feynman or section 26-6 of http://www.feynmanlectures.caltech.edu/I_26.html

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    $\begingroup$ In addition to the previous answer, also in the classical theory light can be seen as a sum over plane waves. For a point B at sufficient distance from a light source A only the plane wave with k-vector in the direction from A to B survives, the others cancel by interference. $\endgroup$ – my2cts May 26 at 17:17

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