Fermat's Principle Fermat's Principle provides another means for determining what happens to a light wave when it either reflects off, or refracts into time. Whenever we need to deal with extrema such as "shortest time," calculus comes into play, so here goes... P. 1. Reflection -- The diagram to the right shows a light ray that starts at point Pi and ends at point P2, after reflecting off a flat surface. Several distances and angles are labeled. a. Derive a formula for the time it takes the light to go from Pi to P in terms of the distances x, y1, y2, and L. Assume the light is travels at speed c. b. Fermat's Principle states that the light will choose a reflective path that minimizes this time function. Every variable in your formula except for x is a constant, determined by the starting and ending points, which are given. The variable x is chosen by the light such that it minimizes t. Use calculus to derive an expression for x that accomplishes this, and show that this answer is equivalent to the Law of Reflection.

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