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.