Given three points one can find a fourth point such that the sum of its distances from the three points is minimal, using any of the many methods available in the literature. The solution point is called Fermat’s Point (FP). The solution points to, two special cases. One is when the triangle formed from the three given points contains an angle equal to 120°. The other is when the triangle contains an angle greater than 120°. In both these cases the sum of the two distances i.e. the sum of the lengths of the sides containing that angle is minimum. This is well known. It is also well known that light travels between two given points by the minimum distance path viz. along the straight line connecting two points. If it suffers reflection at a point enroute, it travels by a two-segment broken line path. The path followed is such that the sum of the two segments is a minimum. The reflection phenomenon is governed by Snell’s law of reflection. Reflection offers us an example of a natural phenomenon with three points and two distances connecting them. Therefore, we can compare the two minimal sums of distances given by FP and Snell’s law. In this paper, we compare them and show that the two results are contradictory. Therefore, it follows that FP violates Snell’s law. Snell’s law of reflection and refraction are so connected that if one is violated the other is also violated.