Using the spectrally resolved white light interferometry we present our experimental results on the measurement of the optical constants of thin polymer films coated on a transparent substrate. As an extension to our previous work (J. Opt. Soc. Am.B12, 1559 (1995)) on thick glass plates, we have shown here that this technique can be effectively applied to very thin polymer films also. We have improved the accuracy of our results by using the Sellmeier dispersion formula for fitting the data. From the width and position of the zero-order fringe and the frequency of modulations in the white light spectrum, the refractive indexn(λ) and thicknesst of the thin polymer films are calculated. To study the accuracies involved in the technique, PVA, PMMA and PS films of varied thicknesses are coated on glass plates and the measured values are compared with ellipsometer studies.