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The reflection of linearly polarized light from an N-layer system of nanometer-size insulating films is investigated. The approximate formulas for reflection coefficients of s- or p-polarized light are derived and their accuracy is estimated. It is shown that expressions obtained for differential reflection characteristics are of immediate interest to the solution of the inverse problem for nanoscopic layered structures. A few novel options are developed for determining the parameters of nanometer-size insulating layers by differential reflectance measurements, particularly at the Brewster angle. For determining the parameters of multilayer systems an appropriate method is found by combining differential reflectance with ellipsometry.