A vector formulation is used to derive an analytical expression for the complex reflectivity of a corner-cube retroreflector, with use of the complex reflection coefficients for the s and p polarization. This expression shows that the corner-cube retroreflector modifies the incoming electric field according to the angle of incidence and the ray path through the retroreflector. The change in the electric field depends on the errors in the surface finish, the coating nonuniformity, and the nonhomogeneity in the index of refraction in the case of the solid corner-cube retroreflector. The main point is that the corner-cube retroreflector conjugates the incident beam only in the case of a plane wave with a constant amplitude incident upon a perfect corner-cube retroreflector. reflectivity, exact ray trace, vector fields.