Light ray

A path of light propagation in the geometrical optics approximation. In a smoothly varying propagation speed, Fermat principle makes its travel time stationary.

For speed $c(y)=y+c_0>0$, Fermat principle and the Beltrami identity yield circular light rays whose centres lie on $y=-c_0$. The ray between $(\pm a,0)$ in the upper half-plane is $y=\sqrt{a^2+c_0^2-x^2}-c_0$.