A method for determining the optical properties of a film on an isotropic substrate is proposed. The method is based on the existence of two specific incidence angles in the angular interference pattern of the p-polarized light where oscillations of the reflection coefficient cease. The first of these angles, theta(B1), is the well-known Abeles angle, i.e., the ambient-film Brewster angle, and the second angle theta(B2) is the film-substrate Brewster angle. In the conventional planar geometry and in a vacuum ambient there is a rigorous constraint epsilon(1) + epsilon > epsilon(1)epsilon on the film and the substrate dielectric permittivities epsilon(1) and epsilon, respectively, for the existence of the second angle theta(B2). The limitation may be removed in an experiment by use of a cylindrical lens as an ambient with epsilon(0) > 1, so that both angles become observable. This, contrary to general belief, allows one to adopt the conventional Abeles method not only for films with epsilon(1) close to the substrate's value epsilon but also for any value of epsilon(1). The method, when applied to a wedge-shaped film or to any film of unknown variable thickness, permits one to determine (i) the refractive index of a film on an unknown substrate, (ii) the vertical and the horizontal optical anisotropies of a film on an isotropic substrate, (iii) the weak absorption of a moderately thick film on a transparent or an absorbing isotropic substrate. (C) 1999 Optical Society of America.381941644171