Fermat's principle assures that the angles given by Snell's law always reflect light's quickest path between P and Q.

Fermat's principle in optics states: Image File history File links File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Snells law - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... See also list of optical topics. ...

The actual path between two points taken by a beam of light is the one which is traversed in the least time.

This principle was first stated by Pierre de Fermat. Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, southern France, and a mathematician who is given credit for the development of modern calculus. ...

Whilst Huygens' principle is useful for explaining diffraction, it is of little use for calculating the properties of light mathematically. Fermat's Principle (as quoted above in its original form) can be used to describe the properties of light-rays reflected off mirrors, refracted through different media, or undergoing total internal reflection. It can be used to derive Snell's law. Huygens principle (named for Dutch physicist Christiaan Huygens) is a method of analysis applied to problems of wave propagation. ... Diffraction is the apparent bending and spreading of waves when they meet an obstruction. ... The word reflection (also spelt reflexion in British English) can refer to several different concepts: In mathematics, reflection is the transformation of a space. ... The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when total internal reflection occurs. ... Snells law - Wikipedia, the free encyclopedia /**/ @import /skins-1. ...

The modern, full version of Fermat's Principle states that the optical path length must be extremal, which means that it can be either minimal, maximal or a point of inflection (a saddle point). Minima occur most often, for instance the angle of refraction a wave takes when passing into a different medium or the path light has when reflected off of a planar mirror. Maxima occur in gravitational lensing. A point of inflection describes the path light takes when it is reflected off of an elliptical mirrored surface. In optics and telecommunication, the term optical path length has the following meanings: In a medium of constant refractive index, n , the product of the geometric distance and the refractive index. ... In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the x-axis or, equivalently, where the derivative of the function equals zero (known as a critical number). ... Saddle point in the graph of z=x²-y² In mathematics, a saddle point is a point of a function of two variables which is a stationary point but not a local extremum. ... Angle of refraction is the angle between the beam refracted at the boundary between two media of different refractive indices and the normal (line perpendicular to the surface at the point of the incidence). ... A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is bent around a massive object (such as a massive galaxy) between the source object and the observer. ... In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the x-axis or, equivalently, where the derivative of the function equals zero (known as a critical number). ... In mathematics, an ellipse (from the Greek for absence) is a plane algebraic curve where the sum of the distances from any point on the curve to two fixed points is constant. ...