A theoretical description of the linear distributions of intensities of radiation reflected from and transmitted through a thin film on a thick, transparent, parallel-sided substrate illuminated with light beam of a finite diameter is given. Results of numerical calculations show the dependences of these distributions on experiment conditions (polarization, wavelength, angle of incidence and spatial distribution of radiation in the incident light beam) as well as on optical and geometrical parameters of the sample (thickness, refractive index and absorption coefficient of the thin film, thickness and refractive index of the substrate). Investigation of the distribution of reflected radiation can be used as a new method of determining optical constants and thicknesses of thin films on thick, parallel-sided, transparent substrates.