We present a theoretical discussion of the optical reflectivity and transmissivity of a dielectric slab of arbitrary thickness, with index of refraction that contains a term proportional to the intensity of the optical wave in the slab. An exact solution is found for the problem, in terms of a single parameter whose value is determined through a straightforward numerical search procedure. We present numerical studies of the power dependence of the transmissivity, with emphasis on bistability, and the multivalued behavior of the transmissivity considered as a function of incident power.