The geometric optics approximation for radiative scattering from rough surfaces is compared with exact scattering predictions from electromagnetic theory. Rigorous electromagnetic scattering theory is numerically formulated based on the extinction theorem. Radiative predictions from one-dimensional random rough surface profiles are calculated for a broad range of surface length scales (correlation lengths, rms roughnesses), wavelengths and incident angles. A directional criterion is used to compare the exact and the approximate results based on very small angular regions. Surface parameter domains for the regions of accuracy of the geometric optics approximation are quantified and presented as a function of surface slope and roughness.