Exact microscopic theory of surface contributions to the reflectivity of a jellium solid

Exact microscopic formulas are derived for the surface optical properties of a jellium solid. The comparison of these formulas to those derived classically by McIntyre and Aspnes shows that for $s$-polarized light, the parametrization of surface-reflectance data using the classical theory is a valid procedure, but that for $p$-polarized light, because short-wavelength fields are induced in the surface region, the classical assumption of local dielectric response is invalid, and thus the classical prescription for parametrizing surface reflectance data is unphysical.