Geometrical optics

Geometrical optics was well reviewed in the electrical-engineering literature by Kouyoumjian (1965) and Deschamps (1972), among many others. It is based on the equality of the angles of incidence and reflection first noticed by the Greeks, and on Snell's sine law for refraction, developed in the 17th century.

Fermat's principle, which states that the optical length

$$S(C)=\int_{C}n d\sigma$$

must be stationary for the ray curve $C$ joining two points, embodies both of these principles, and forms the basis for optical ray-tracing schemes.

In terms of seismology,

$$S(C)=\int_C \frac{{\rm d}s}{v} .$$

This equation can be used for basic ray tracing schemes; however, such schemes based on Fermat's principle provide no amplitude information.