  Geometrical optics (GO) is widely used in studies of electromagnetic
materials because of its ease of use compared to full-wave numerical
simulations. Exact solutions for waves can, however, differ significantly from
the GO approximation. In particular, effects that are "perfect" for waves
cannot usually be derived using GO. Here we give a method for designing
materials in which GO is exact for some waves. This enables us to find
interesting analytical solutions for exact wave propagation in inhomogeneous
media. Two examples of the technique are given: a material in which two point
sources do not interfere, and a perfect isotropic cloak for waves from a point
source. We also give the form of material response required for GO to be exact
for all waves.
