We develop an optical model for absorption enhancement and diffuse reflectance by metal nanoparticles on a silicon waveguide. A point dipole treatment is used, including the effects of the waveguide on both the angular emission spectrum and scattering cross section of the dipoles. The model agrees very well with our experimental results of greatly enhanced electroluminescence and photocurrent from silicon-on-insulator light-emitting diodes and also gives very good agreement with previously reported diffuse reflectance measurements. The results suggest that the main mechanism in the enhancement of diffuse reflectance in this system is a dramatic enhancement in the scattering cross section of waveguided light, rather than a waveguide-mediated dipole-dipole interaction. We also put lower bounds on the radiative efficiency of scattering by the nanoparticles.