The infrared spectral reflectance of a semi-infinite medium composed of irregular particles of different materials is calculated in terms of the sizes, shapes, and complex refractive indices of the particles. For particles larger than the wavelength, the scattering and absorption are computed mainly by geometrical optics but with important wave-optical corrections for the additional absorption caused by edges and asperities, which are represented by dipoles distributed over the surface of the particle. For particles smaller than the wavelength, a Lorentz-Lorenz model is used to derive the average complex index of the medium, the particles being treated as ellipsoids with a wide range of shapes. The average scattering of an individual ellipsoidal particle is then found from the relative refractive index of the particle with respect to the Lorentz-Lorenz medium. For both large and small particles the single-particle scattering is represented by six discrete beams. Calculation of the reflectance is then facilitated by a radiative transfer method that also involves six beams. For particles of intermediate size a suitable formula bridging the results for large and small particles is found to be satisfactory.