A simple model of a gravitational lens from geometric optics

We propose a simple geometric optics analog of a gravitational lens with a refractive index equal to one at large distances and scaling like n(r)2=1+C2/r2, where C is a constant. We obtain the equation for ray trajectories from Fermat's principle of least time and the Euler equation. Our model yields a very simple ray trajectory equation. The optical rays bending, reflecting, and looping around the lens are all described by a single trigonometric function in polar coordinates. Optical rays experiencing fatal attraction are described by a hyperbolic function. We use our model to illustrate the formation of Einstein rings and multiple images.