A self-consistent tight-binding technique has been employed to calculate the electronic structures of the Sb - and Sn - Si surfaces. For the Sn reconstructed surface, two filled and one unfilled surface states as well as one straddling the Fermi level were calculated. Three filled and two unfilled surface states were calculated for the Sb reconstructed surface. These surface state positions are in good agreement with experiments. We have also calculated the imaginary part of the surface dielectric function, , the surface dielectric function anisotropy and the corresponding reflectance anisotropy spectra for these reconstructed surfaces. For comparison we have also calculated the difference between the imaginary parts of the surface dielectric functions for the Sn - Si and Si surfaces.