Fermat's Principle:Reflection
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:
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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.
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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.
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Index
Reflection concepts
Mirror concepts |