  We consider the Casimir effect for a scalar field interacting with another
scalar field that is confined to two half spaces. This model is aimed to mimic
the interaction of the photon field with matter in two slabs. We use Dirichlet
boundary conditions on the interfaces for the fields in the half spaces and
calculate their one-loop contribution to the wave equation for the other field.
We perform the ultraviolet renormalization and develop a convenient formalism
for the calculation of the vacuum energy in this configuration.
