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The diagonal component ɛxx and off-diagonal component ɛxy of the complex dielectric tensor for the ferromagnetic compound NiMnSb are determined using ex situ spectroscopic ellipsometry and magneto-optic analysis over the spectral range from 0.7 to 6.2 eV. The effects of the overcoat on the raw data are removed by the analysis. First, the complex ɛxx of thin-film NiMnSb were determined by ex situ spectroscopic ellipsometry; then ɛxy was determined by analyzing Kerr rotation and ellipticity data using the determined ɛxy data. Lorentz oscillators were used to model peaks seen in the ɛxx spectra. The diagonal dielectric component ɛxx is dominated by free-carrier effects below 1.15 eV, and dominated by interband transitions above 2.0 eV. The center energies of the Lorentz oscillators are consistent with the calculated band structure and minority-spin optical conductivity of NiMnSb. Joint density of states and optical conductivity calculated from ɛxx (2) data with free-carrier effects removed shows onset energies at ~ 0.6 and ~ 0.2 eV, respectively. From a study of the ɛxx and ɛxy spectra, the Kerr rotation peak at lower energy is determined to be due to combined contributions from: (1) a crossover between the free-carrier effect and interband transitions, and (2) transitions involving spin-orbit coupling. The high-Kerr rotation peaks at higher energies result exclusively from transitions involving spin-orbit coupling.