Polarisation-entangled photon pairs from a two crystal, type-I spontaneous parametric down conversion source are used to make accurate measurements of the ellipsometric angles of a silicon dioxide film on silicon and of internal and external reflection from BK7 glass. Since our source produces an entangled state with some mixture, a novel technique based on quantum tomography was developed to estimate the components of the density matrix for the state before and after reflection from the samples. The ellipsometric angles are readily calculated from these components and experimental measurements made on the samples were found to be in good agreement with their expected values.