According to Fermat's principle, the actual path taken by a light ray in space locally minimizes the "optical length". It is possible to use the optical length (for some given function n) to defined a new geometry whose geodesic curves are the paths taken by light rays. This is a particular type of Riemannian geometry, called "conformally" Euclidian
One of the most famous paintings of Escher show a disc filled with little angels and demons crowding towards the boundary circle. What refractive index would produce the metric distortions shown in that picture?
