Focusing virtual photons: Casimir energies for some pairs of conductors

We consider the Casimir energy of a pair of conductors, for parallel plates, vertical-bar-o for a plate and a sphere, oo for two separated spheres, and for one sphere inside the other. We also obtain (o for an open shell and a sphere, a configuration which might be experimentally preferable. Semiclassically the Casimir energy is given by the optical properties of the system of coaxial mirrors, with focal lengths f1 and f2, a distance lf1, f2 apart. It is proportional to b, with 1/b = 1/f1 + 1/f2-l/(2f1f2) = 2h/(lf12), when f12 is the focal length of the system and h is the distance between the object and image planes with unit lateral magnification.