Here Fermat's Principle of Least Time use to prove geometrically the law of light reflection. AX finish start The time between the points can be expressed as: t= hi+tr = di do _ Vai + zi va} + z? _vaitz, V(Ax -x1)2 + 2, V1 Ur V1 Remember, if we're trying to find the minimum (or maximum) of a function, we differentiate with respect to the variable of interest and set the resulting expression to zero: Ot 0 = 7 Ar - C1 0 = vivaitz v. V (Ax - x1)2 + 2? Recognizing that Ax - 21 = x, and substituting for di and d, yields: Urd, Or, in terms of the angles: sin 1 sin Or U1 Ur Since v1 = v., as both paths are in the same phase, this simplifies to our known law for refraction: 01 = 07. Apply this approach to derive Snell's Law