We present a new theoretical analysis of a harmonic model of a polarizable fluid. In this Drude oscillator model, particles with classical mechanical translational degrees of freedom contain internal quantum harmonic oscillators, representing electronic degrees of freedom, which are coupled by dipolar interactions. We relate the calculation of optical properties such as the density of states and the absorption spectrum at finite wave vector to the determination of a Green’s function. A graphical analysis of this Green’s function is shown to suggest a hierarchy of approximations. Calculations based on two members of this hierarchy are compared to recently published simulations of optical properties for this model. Because of the long range of dipolar interactions, this model shows interesting optical properties even in the limit of low particle number density. Our method is shown to agree well with simulation data in this limit.