The reflectivity and reflectance anisotropy (RA) spectra of five silicon surfaces [(001), (113), (112), (111), and (110)] are calculated using the discrete dipole model. The structures used have bulk-terminated surfaces so that RA is found at the optical gap and above. A comparison is made between experimental RA spectra of H-covered (001), (113), and (110) surfaces and the discrete dipole spectra, and it is found that there is agreement for the (001) and (110) surfaces but the best fit to the experimental (113) surface spectrum is found for a (112) surface discrete dipole calculation. RA spectra are obtained using the McIntyre-Aspnes three-layer model with surface layer and bulk dielectric functions taken from discrete dipole calculations. Surface excess dielectric functions are shown for these surfaces. It is found that, although RA spectra of the different surfaces are quite distinct, the gross features of the surface excess dielectric functions that are used to calculate them are quite similar. Thus small shifts in maxima and minima and differences in strength of these functions are responsible for the observed optical anisotropy, rather than distinct spectral features that differ from surface to surface. The surface dielectric function converges to the bulk value within 10 to 20 \AA{} of the vacuum-solid interface, depending on frequency, so that RA at frequencies corresponding to the optical gap energy and above arises from this 20 \AA{} region, rather than the topmost surface layer or layers.