We have investigated the optical properties of internally mixed aerosol particles composed of dicarboxylic acids and ammonium sulfate using cavity ring-down aerosol extinction spectroscopy at a wavelength of 532 nm. The real refractive indices of these nonabsorbing species were retrieved from the extinction and concentration of the particles using Mie scattering theory. We obtain refractive indices for pure ammonium sulfate and pure dicarboxylic acids that are consistent with literature values, where they exist, to within experimental error. For mixed particles, however, our data deviates significantly from a volume-weighted average of the pure components. Surprisingly, the real refractive indices of internal mixtures of succinic acid and ammonium sulfate are higher than either of the pure components at the highest organic weight fractions. For binary internal mixtures of oxalic or adipic acid with ammonium sulfate, the real refractive indices of the mixtures are approximately the same as ammonium sulfate for all organic weight fractions. Various optical mixing rules for homogeneous and slightly heterogeneous systems fail to explain the experimental real refractive indices. It is likely that complex particle morphologies are responsible for the observed behavior of the mixed particles. Implications of our results for atmospheric modeling and aerosol structure are discussed.