Elementary approximate derivations of some retarded Casimir interactions involving one or two dielectric walls.

The original derivation by Lifshitz [Sov. Phys. 2, 73 (1956)] of P DD , the force per unit area between two plane parallel dielectric walls, is ertremely complicated; the later derivations are simpler but still difficult. The standard derivation of the interaction V AtD of an atom and a dielectric wall uses the expression for P DD as its starting point. The results are valid for all values of the separation l. For l∼∞, where the interactions are retarded, we obtain reasonably accurate approximate expressions for P DD and for V AtD -and also for V ElD , the retarded interaction of an electron and a dielectric wall-by the elementary procedure of assuming simple forms with one or two open parameters, adjusted to give the known results for retarded interactions which do not include dielectric walls