Optical path length

The optical path length  L (also known as the optical path ) in wave optics is the path length for which light in a vacuum needs the same time as for a given path with a possibly different phase velocity (the speed with which the wave fronts of the light advance).

The difference between the optical path lengths of two paths is called the path difference , see applications there.

calculation

The ratio of the speed of light in a vacuum to the phase speed in the medium is the refractive index n of the medium. If this is constant in sections on the given path, such as the beam path through a lens system , then the optical path length is a sum over the sections : ${\displaystyle c_{0}}$ ${\displaystyle c_{\mathrm {M} }}$  ${\displaystyle s_{i}}$

${\displaystyle L=\sum n_{i}\cdot s_{i}\,.}$

If, on the other hand, the refractive index varies from place to place, for example in the case of a mirage , the following generally applies:

${\displaystyle L=\int n(s)\cdot \mathrm {d} s\,.}$

See also

• Fermat's principle
• Optical thickness

Individual evidence

1. ^ Max J. Riedl: Optical Basics for Infrared Systems (= Tutorial Texts in Optical Engineering. 56). SPIE Press, Bellingham WA 2002, ISBN 0-8194-4499-5 , p. 80 ( limited preview in Google book search).