Fermat's principle, also known as the principle of least time, is a fundamental concept in optics formulated by the French mathematician Pierre de Fermat in the 17th century. It states that the path taken by a ray of light between two points is the one that can be traversed in the least time.
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Fermat's principle characterizes a light ray between fixed endpoints by stationary travel time, or stationary optical path length in a stationary isotropic medium. With refractive index and path element , the travel time is , so an allowed ray has vanishing first variation of this integral. Stationary does not always mean the globally shortest time.
For a planar interface between two uniform media, vary the point at which a broken straight path crosses the interface. Setting the travel-time derivative to zero gives , Snell's law, with angles measured from the normal. This makes the link between a variational statement and an observable direction of refraction explicit. The geometrical optics description requires scales large enough compared with the wavelength; diffraction supplies effects that a single ray cannot describe.