  We propose a new approach to the Casimir effect based on classical ray
optics. We define and compute the contribution of classical optical paths to
the Casimir force between rigid bodies. We reproduce the standard result for
parallel plates and agree over a wide range of parameters with a recent
numerical treatment of the sphere and plate with Dirichlet boundary conditions.
Our approach improves upon proximity force approximation. It can be generalized
easily to other geometries, other boundary conditions, to the computation of
Casimir energy densities and to many other situations.
