What is the Fermat Principle

Snellius’s law of refraction

Fermat’s principle


The propagation of the light takes place between two points A and B of a medium on that path for which the required time is a minimum:



Because n = c / v one obtains with ds = n.dl as optical path length:



With the help of Fermat’s principle, for example, Snellius’s law of refraction can be derived:

The light beam should go from point A to point B. The position of point P is varied until the time to run through the distance

A-P-B becomes a minimum.


The total time results in



The time should be minimal, i.e.



With sina = x / s1 and sinb = (x2-x) / s2 that follows




If the refractive index changes continuously, e.g. in warmed layers of air, a curvature of light takes place.

In the case of a very shallow incidence on an optically thinner medium (heated air), a quasi total reflection.