In this paper the set of parameters (n(f), k(f), d(f)) Of homogeneous isotropic films deposited on known semi-infinite substrates are examined which provide measured values of the ellipsometric angles Psi and Delta. A transformation of the IEP transcendental equation to a differential equation is considered, and the 'step by step movement' numerical method of solution search is suggested. Our approach has made it possible to discover families of three-dimensional curves in the film parameter space, all points of which are exact solutions for the measured pair of ellipsometric angles Psi and Delta. The solutions found include 'exotic' ones such as those for which k(f) < 0. We believe the study of the general features of these solutions allows us to achieve an understanding of difficulties of minimization procedures.