Focusing virtual photons: Casimir energies for some pairs of conductors

We consider the Casimir enemy E of a pair of conductors, E-\\ for parallel plates, E-\0, for a plate and a sphere, E-00 for two separated spheres, and E-. for one sphere inside the other. We also obtain E-(0 for an open shell and a sphere, a configuration which might be experimentally preferable. Se miclassically the Casimir energy is given by the optical properties of the system of coaxial mirrors, with focal lengths f(1) and f(2), a distance l m uch less than f(1), f(2) apart. It is proportional to b, with 1/b = 1/f(1) + 1/f(2) - l/(2f(1)f(2)) = 2 Delta h/(lf(12)), when f(12) is the focal leng th of the system and Delta h is the distance between the object and image p lanes with unit lateral magnification.