What is the Fermat Principle
Snellius’s law of refraction
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.
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