  In this paper we take a deeper look at the technically elementary but
physically robust viewpoint in which the Casimir energy in dielectric media is
interpreted as the change in the total zero point energy of the electromagnetic
vacuum summed over all states. Extending results presented in previous papers
[hep-th/9609195; hep-th/9702007] we approximate the sum over states by an
integral over the density of states including finite volume corrections. For an
arbitrarily-shaped finite dielectric, the first finite-volume correction to the
density of states is shown to be proportional to the surface area of the
dielectric interface and is explicitly evaluated as a function of the
permeability and permitivity. Since these calculations are founded in an
elementary and straightforward way on the underlying physics of the Casimir
effect they serve as an important consistency check on field-theoretic
calculations. As a concrete example we discuss Schwinger's suggestion that the
Casimir effect might be the underlying physical basis behind sonoluminescence}.
The recent controversy concerning the relative importance of volume and surface
contributions is discussed. For sufficiently large bubbles the volume effect is
always dominant. Furthermore we can explicitly calculate the surface area
contribution as a function of refractive index.
