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We have investigated optical properties of thermally grown SiO2 layers within the thickness range 150 to 500 nm. The complex dielectric constant ε(ν˜) can be represented by six Lorentz-Gauss oscillators, which allow us to determine the optical constants of SiO2 films by fitting IR transmittance spectra. The spectra of ε(ν˜), unlike transmittance, are not affected by the multiple reflections at the film/air and film/substrate interfaces. Changes of optical constants for different thicknesses can be attributed to changes of physical properties of the film. We compare dielectric functions of samples oxidized at different conditions and discuss the influence of thickness and surface preparation of the substrate. We also compare our results with the dielectric function of bulk vitreous silica.