Fermat's principle

English

Alternative forms

• Fermat's principle of least time
• principle of least time

Etymology

First proposed by French mathematician Pierre de Fermat in 1662.

Proper noun

Fermat's principle

1. (physics, optics) The principle, which links geometrical optics (or "ray optics") with wave optics, that the path traversed by a ray between two given points is: (in the original "strong" formulation) the one that takes the least time, or (in a weaker but more general formulation) one that takes a time that is "stationary" with respect to variations of the path (so that, loosely speaking, a small change in the ray path entails a very small change in the traversal time).
   • 1960, John Clarke Slater, Quantum Theory of Atomic Structure, McGraw-Hill, page 39:

     But we now see that, if we use Fermat's principle, a fundamental result of any wave theory, and combine it with de Broglie's assumption about the relation between momentum and wavelength, we are led at once to the principle of least action.

   • 1968, Petr Beckmann, The Depolarization of Electromagnetic Waves, Golem Press, page 108:

     […] , Keller simply postulates these rays and finds their direction from Fermat's principle adapted to the hypothesis that these rays exist.

   • 1976, Donald E. Tilley, Walter Thumm, Physics for College Students, Cummings Publishing Company, page 558,

     […] students wishing to pursue this branch of physics further will find that refraction too can be explained in terms of Fermat's principle.

Translations

principle in optics

• French: principe de Fermat m
• German: Fermatsches Prinzip n
• Italian: please add this translation if you can

See also

• principle of least action