Fermat's Principle: Light follows the path of least time. Of course the straight line from A to B is the shortest time, but suppose it has a single reflection. The law of reflection can be derived from this principle as follows:
The pathlength from A to B is
Since the speed is constant, the
minimum time path is simply the minimum distance path. This may be found by setting the derivative
of L with respect to x equal to zero.
|This reduces to||which is|
This derivation makes use of the calculus of maximum-minimum determination, the derivative of a square root, and the definitions of the triangle trig functions.