Focusing Virtual Photons: Casimir Energies for Some Pairs of Conductors

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Abstract
We consider the Casimir energy E of a pair of conductors, E( parallel) for parallel plates, E(|o) for a plate and a sphere, E(oo) for two separated spheres, and E( middle dot in circle) for one sphere inside the other. We also obtain E((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 f(1) and f(2), a distance l<<f(1),f(2) apart. It is proportional to b, with 1/b = 1/f(1)+1/f(2)-l/(2f(1)f(2)) = 2Deltah/(lf(12)), where f(12) is the focal length of the system and Deltah is the distance between the object and image planes with unit lateral magnification.

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