A three-dimensional model has been developed for simulating Saharan dust emissions and transport over the tropical North Atlantic Ocean. The computed dust fields are constrained by data from ACE-2, and we use a radiative transfer code to simulate the Total Ozone Mapping Spectrometer on the Earth Probe satellite (EP-TOMS) aerosol index (AI). Using the observed relationship between AI and aerosol optical depth, we determine from our simulations the UV refractive index for dust particles at Dakar, Sal, and Tenerife. We find that the dust imaginary refractive index at Sal and Tenerife is approximately k = 0.0048 (0.0024--0.0060) at 331 nm and k = 0.004 (0.002--0.005) at 360 nm. At Dakar the dust imaginary refractive index is approximately k = 0.006 (0.0024--0.0207) at 331 nm and k = 0.005 (0.0020--0.0175) at 360 nm. These values are considerably less absorbing than the refractive index currently used in the TOMS retrievals of dust optical depth and single scatter albedo. Once the dust refractive index has been constrained, we calculate the single scatter albedo by integrating across the particle size distribution. We find that the particle single scatter albedo at 331 nm is ϖ0 = 0.81 (0.65--0.90) at Dakar, ϖ0 = 0.84 (0.82--0.91) at Sal, and ϖ0 = 0.86 (0.83--0.89) at Tenerife. The refractive index determined in this study should be useful for future retrievals using the TOMS data, as well as for energy balance studies that incorporate the radiative effects of mineral dust aerosols.