Using nonstandard recursion relations for Fresnel coefficients involving
successive stacks of layers, we extend the Lifshitz formula to configurations
with an inhomogeneous, n-layered, medium separating two planar objects. The
force on each object is the sum of a Lifshitz like force and a force arising
from the inhomogeneity of the medium. The theory correctly reproduces very
recently obtained results for the Casimir force/energy in some simple systems
of this kind. As a by product, we obtain a formula for the force on an
(unspecified) stack of layers between two planar objects which generalizes our
previous result for the force on a slab in a planar cavity.Comment: 5 pages, 1 figure, presented at QFEXT1