The chemical reaction of a sample with atmospheric gases causes a significant error in the determinantion of the complex refractive index n = 1 - delta + ibeta in the extreme-ultraviolet region. The protection of samples removes this effect but hampers the interpretation of measurements. To overcome this difficulty, we derive the exact dependences on film thickness of the reflectivity and transmissivity of a protected film. These dependences greatly simplify the determination of delta and beta when the spectra of several films with different thickness and identical protection are measured. They also allow the verification of the delta(omega) obtained from the Kramers-Kronig relation and even make the Kramers-Kronig method unnecessary in many cases. As a practical application, the optical constants of Sc and Ti are determined at h omega = 18-70 eV and 18-99 eV, respectively. The essential feature of our experimental technique is deposition of a film sample directly on a silicon photodiode that allows easy operation with both thin (approximately 10-nm) and thick (approximately 100-nm) films. The comparison of calculated reflectivities of Si-Sc multilayers with the measured values shows the high accuracy of the determined delta(omega) and beta(omega).