A technique is described wherein reflectivity data taken at two angles of incidence are used to obtain pertinent information on the optical fine structure of the rare-earth iron garnets. The complex index of refraction is determined for GdIG and TbIG over an energy range of 2 to 5 eV. From this data the absorption coefficient is calculated, and by approximating the absorption characteristic with a series of Lorentzian shaped lines detailed information such as transition oscillator strength and excited state lifetimes is obtained. In general the fine-structure oscillator strengths are found to be

and lifetimes are

. The data show some evidence of the presence of rare-earth ion transitions in the spectra, and the possibility of optical pumping to effect a change in Tb sublattice magnetization in TbIG is discussed.