The sum rule for the imaginary part of the dielectric function epsilon" can help in discriminating surface and bulk-related optical transitions, by means of the number of electrons taking part in the transitions. This is particularly simple in the region below the main critical points of the bulk band structure (below 3.5 eV for Si, below 2.2 eV for Ge), since there the surface differential reflectivity is roughly proportional to epsilon" of the surface. We discuss the cases of Ge(1 1 1)-2 x 1 and Si(1 1 1)-2 x 1 investigated by surface differential reflectivity in the energy range 0.3-3.5 eV, with light linearly polarized parallel and perpendicular to the chains of the Pandey model. A key point is that the sum rule holds for each polarization separately (termed alpha and beta), implying that: integral omega epsilon (")(alpha)d omega = integral omega epsilon (")(beta)d omega. In these results, the effect of the sum rule can be easily recognized (crossing of the curves and seemingly equal areas on both sides of the crossing point). Similar considerations should also hold for reflectance anisotropy spectroscopy (RAS). It will be shown, however, that a compensation of positive and negative signals, in compliance with the sum rule, is actually expected only if RA spectra are multiplied by a suitable function. Moreover, the compensation is not exact, when the bulk is strongly absorbing. The results of a numerical simulation valid for various materials and surface oscillators are reported. They help to understand why in some cases (for instance in GaAs(0 0 1)-2 x 4 and -4 x 2), the sum rule is apparently not obeyed.