The thickness of films (<900 Å) of silicon dioxide on silicon can be determined by observation near Brewster's angle for silicon with the light polarized in the plane of incidence. Since the intensity of the reflected light increases with thickness for these films, the measurement is made by direct comparison of the light reflected by a sample with a calibrated SiO2on silicon ``thickness gauge.'' Film thicknesses can be estimated to an accuracy of about±30 Å for thicknesses less than 150 Å and±50 Å for thicknesses between 150 Å and 900 Å.