The refractive indices of short-period binary (AlAs)m(GaAs)n superlattices, where m = n, were investigated by measuring the beam divergences of optical waveguides using these superlattices as the core material. It is demonstrated that the refractive index depends on the period of the superlattice and not simply on the average composition. The refractive index is shown to depend in a systematic way on the direct bandgap of the superlattice, although the relationship may not be quite the same as that for a random alloy.