Cloud microphysical and optical properties are inferred from the bidirectional reflectances simulated for a single-layered cloud consisting of an external mixture of ice particles and liquid droplets. The reflectances are calculated with a rigorous discrete ordinates radiative transfer model and are functions of the cloud effective particle size, the cloud optical thickness, and the values of the ice fraction in the cloud (Le. the ratio of ice water content to total water content). In the present light scattering and radiative transfer simulations, the ice fraction is assumed to be vertically homogeneous; the habit (shape) percentage as a function of ice particle size is consistent with that used for the Moderate Resolution Imaging Spectroradiometer (MODIS) operational (Collection 4 and earlier) cloud products; and the surface is assumed to be Lambertian with an albedo of 0.03. Furthermore, error analyses are performed that pertain to the inference of the mixed-phase cloud effective particle size and optical thickness. Errors are calculated with respect to the assumption of a cloud containing solely liquid or ice phase particles. The analyses suggest that the effective particle size inferred for a mixed-phase cloud can be underestimated (or overestimated) if pure liquid phase (or pure ice phase) is assumed for the cloud, whereas the corresponding cloud optical thickness can be overestimated (or underestimated).