Dispersion relations for complex reflectivities*†

A simplified derivation of the dispersion relations connecting the phase and amplitude of the normal optical reflectivity of a vacuum-matter interface is presented. The non-Kramers-Kronig form of the expression for reflectivity in terms of phase is shown to be a consequence of the fact that amplitudes are determined only up to a multiplicative constant by the phase. The phase, however, is uniquely determined by the amplitude.