From Snell's law to Fermat's principle

Suppose high frequency sound propagates from a point source in an inhomogeneous medium by ray theory. This paper shows how Snell's law and its generalizations can be used to prove Fermat's principle of least time, provided that we restrict to the region free from caustics. Also if the sound speed is a concave function of position it is shown that caustics do not occur so Fermat's principle applies without further restriction.

Automated summary

This paper demonstrates how ray theory can explain the propagation of high frequency sound waves from a point source in an inhomogeneous medium, and how Snell's law and its generalizations can be used to prove the principle of least time according to Fermat, with restrictions applied to the region free from caustics. It is also shown that if the sound speed is a concave function of position, caustics do not occur and Fermat's principle can be applied without further restriction.