Casimir energy for a hyperboloid facing a plate in the optical approximation -: art. no. 012105

We study the Casimir energy of a massless scalar field that obeys Dirichlet boundary conditions on a hyperboloid facing a plate. We use the optical approximation including the first six reflections and compare the results with the predictions of the proximity force approximation and the semiclassical method. We also consider finite size effects by contrasting the infinite with a finite plate. We find sizable and qualitative differences between the optical method and the more traditional approaches.