The optical properties and hence the radiative forcing of atmospheric aerosols are determined, in part, by the way in which the various constituents are externally or internally mixed. The mixing state must be known to compute the effective refractive index, water activity, and size distribution of the aerosols. In this study we found that the percentage difference in the optical properties, including extinction, single scattering albedo, and asymmetry parameter, between an internal mixture and external mixture of black carbon and ammonium sulfate can be over 25% for the dry case and over 50% for the wet case for typical mass mixing ratios. The differences are a result of a complicated combination of nonlinear Mie theory on the refractive index, assumptions about the coagulated particle sizes for internal mixtures, and the role of water uptake and deliquescence as a function of relative humidity. The computed optical properties are used to estimate the globally average clear-sky direct radiative forcing for different mixing assumptions. The results are displayed as a function of relative humidity to conveniently see the mixing effects for dry aerosols at less than the crystallization point, for dry internal and wet external mixtures between the crystallization and deliquescence points, and for fully wet mixtures above the deliquescence point. For a 9:1 ammonium sulfate to black carbon mass ratio, nearly all the cooling effect predicted for an external mixture is lost for the internally mixed assumption, especially for relative humidities less than the deliquescence point.