A simple experiment to determine the complex refractive index of a semiconductor in thin film form through transmittance measurements is presented. The experiment allows us to obtain, from the real part of the refractive index, thendispersive law, and from the imaginary part, the absorption coefficient α. An energy dependence analysis of α is done to obtain the semiconductor band gap value and the nature of the optical transition (direct or indirect). Transmittance data of a CdS thin semiconductor film have been analyzed, and a value for the real part of the refractive index, which is very similar to the bulk value, has been obtained. Also, from the absorption coefficient a band gap value of (2.33±0.02) eV for CdS is deduced, in agreement with previously published values.