We present a general method for extracting optical constants n and k plus film thickness t of weakly absorbing materials that exhibit film thicknesses in the micrometer range. This method utilizes the simultaneous fit of multiple transmission measurements of different film thicknesses and employs the constraint that the frequencies of the corresponding measured interference patterns in the nonabsorbing wavelength region have to be matched by means of n, its derivative n' at a certain value E0, and t. Applying this method in practice, we calculate, in two different, independent ways, the optical constants of muscovite mica at 330-800 nm for thicknesses that range from approximately 5 to approximately 160 microns.