Past exam of the physics 2 paper of the University of Oxford / 2013 / 9 / 1

Fermat's principle says that the travel time, or equivalently the optical path length, is stationary under small path variations at fixed endpoints. For a flat interface, let the ray cross at horizontal coordinate $x$, with source and detector at heights $h_1,h_2$ and horizontal separation $D$. Apart from $1/c$, its travel time isSetting $d\mathcal{L}/dx=0$ givesThe angles are measured to the normal. This is Snell's law; “least time” is more generally a stationarity condition.