In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light.[1] However, this version of the principle is not general; a more modern statement of the principle is that rays of light traverse the path of stationary, not minimal, time.Fermat's principle 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 deduced from Huygens' principle, and can be used to derive Snell's law of refraction and the law of reflection.

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Fermat's principle 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 deduced from Huygens'

principle, and can be used to derive Snell's law of refraction and the

law of reflection.

The historical form of the French mathematician Pierre de Fermat is

incomplete. The modern, full version of Fermat's principle states that the

optical path length must be stationary, which means that it can be either

minimal, maximal or a point of inflection (a saddle point). Minima occur

when a wave passes from medium into another refraction and in the reflection

of light from a planar mirror. Maxima occur in gravitational lensing. A point of

inflection describes the path light takes when it is reflected off an elliptical

mirrored surface  !!!!