We calculate the surface dielectric anisotropy (SDA) and the reflectance anisotropy of the relaxed Cu-(110) surface using the ab initio self-consistent full potential linear-muffin-tin orbital method within the local-density approximation. Besides interpreting the spectra in terms of transitions involving surface and/or bulk states, we carry out a depth depending scanning of them, from surface to bulk, with the resolution of one atomic layer. We show that the SDA mainly arises in the vacuum region above the surface and in the first atomic layer.