Fermat's principle

Fermat's principle in optics states:

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

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This principle was first stated by Pierre de Fermat.

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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.

Related Topics:
Huygens' principle - Diffraction - Reflected - Total internal reflection - Snell's law

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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.

Related Topics:
Optical path length - Point of inflection - Saddle point - Angle of refraction - Gravitational lensing - Elliptical

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