Fermat's principle
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Fermat's principle in optics states:
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.
Fermat principle can be considered as a mathematical consequence of Huygens' principle. Indeed, of all secondary waves (along all possible paths) the waves with the extrema (stationary) paths contribute most due to constructive interference.
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. Similar to Huygen's principle it can be used to derive Snell's law of refraction and the law of reflection.
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.
Fermat's principle can be derived from Quantum Electrodynamics and thus is a consequence of Quantum mechanics.
In classic mechanics of waves Fermat principle follows from extremum principle of mechanics (see variational principle).de:Fermatsches Prinzip el:Αρχή του Fermat es:Principio de Fermat it:Principio di Fermat he:עקרון פרמה nl:Principe van Fermat ja:フェルマーの原理 pl:Zasada Fermata ru:Принцип Ферма zh:費馬原理