The reflection of electrons by standing light waves, i.e., the stimulated Compton scattering proposed by Kapitza and Dirac, has been treated by applying the Born approximation. The probability that an electron will be reflected is derived, for light waves that are not too intense, as a function of the electron beam orientation and of the coherence properties of the light waves. It is shown, among other things, that the original formula of Kapitza and Dirac is not directly applicable to representative studies using lasers. More general formulas are given along with a discussion intended to serve as a practical guide in the design of experiments.