The reflectance anisotropy (RA) spectrum of the Si(100)1X2-As surface is calculated using the discrete dipole model. The semiconductor is treated as a slab of pointlike dipole-polarisable bonds coupled by dipolar electrostatic fields. The response of the polarisable bonds to light in normal incidence is expressed in terms of the normal modes of the polarisable bonds which are called dipole waves. These may be classified as surface-localised, surface resonance and bulk dipole waves. We give an analysis of the optical response of this surface in terms of dipole moments localised on bonds that would be too cumbersome to implement using a band structure. The discrete dipole RA spectrum is compared to the experimental spectrum for this surface and a density functional calculation of the spectrum. The discrete dipole spectrum contains the same features as experiment. The origin of the peaks in the RA spectrum is discussed in terms of excitation of dipole waves polarised parallel and perpendicular to the arsenic dimer axes and also in terms of excitation of dipole moments in particular bonds. Parameters for the calculation were obtained from ab initio calculations on clusters.