Comment on "Casimir energies with finite-width mirrors"

We comment on a recent publication [1] by Fosco, Lombardo and Mazzitelli on Casimir energies for material slabs (`finite width mirrors') and report a discrepancy between results obtained there for a single mirror and some previous calculations. We provide a simple consistency check which proves that the method used in [1] is not reliable when applied to approximations of piecewise constant profile of the mirror. We also present an alternative method for calculation of the Casimir energy in such systems based on our recent work. Our results coincide both with perturbation theory and with some older \cite{Bordag'95} and more recent \cite{Vassilevitch'08} calculations, but differ from those of [1].