Here Fermat's Principle of Least Time use to prove geometrically the law of light reflection. Ax finish start di The time between the points can be expressed as: t= hittr = d1 do _ Vait zil val + z? _vaitz , V(x -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: at 0 = 7 Ox1 Ar - 1 0 = vivaitz vr V(Ax - 21)2 + 2, Recognizing that Ax - 21 = x, and substituting for di and d, yields: C1 vidi vrdo Or, in terms of the angles: sin 1 sin Or V1 Ur Since v1 = vr, as both paths are in the same phase, this simplifies to our known law for refraction: 01 = 07. Apply this approach prove the Rectilinear Propagation of light