Atmospheric mineral dust is an important component of the Earth system, affecting climate and biogeochemical cycling. We present an inverse method of inferring dust composition from wavelength dependence of light absorption and the complex refractive indices of aerosol components. Specifically, we separate absorption by black carbon from absorption by hematite and organic carbon. We apply this method to coarse-mode-dominated Aerosol Robotic Network (AERONET) observations in the "dust belt" region of the globe, and we identify differences between dust optical properties and composition in different locations. We solve for dust composition using two opposite, bracketing hypotheses of the state of mineralogical mixing: purely internal mixing and purely external mixing. We find that calculated absolute hematite concentrations are highly sensitive to mixing assumptions, while relative geographic and seasonal patterns are less sensitive to mixing assumptions. Internal mixing calculations appear to underestimate absolute hematite concentrations, while external mixing overestimates hematite concentrations. Inversions calculated assuming external mixing are better able to explain the wavelength dependence of dust absorption by only varying hematite concentration than inversions using internal mixing, which require substantial covariation between black carbon and hematite to match observations. Saharan and East Asian dust show higher hematite content than dust from Arabia. Saharan dust also shows seasonal variation in hematite content which may reflect seasonal shifts in dust source areas.