What is the quickest way for light to get from point *A* to point *B*? The speed of light varies with the medium through which it travels. The quickest route through any one medium is a straight line segment. The only question is where on the boundary should the refraction point be? In this sketch, let *x* be the horizontal distance from *A* to the refraction point. Time is distance divided by speed.

The time will be minimized where the derivative of time with respect to *x* is zero.

This last equation is a version of Snell’s Law. If light (or anything else) conforms to Snell’s Law, then it must be taking the quickest path.

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Last update: August 3, 2011 ... Paul Kunkel *whistling@whistleralley.com *

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