The problem of the scattering (reflection and transmission) of light by multi-layer magnetic and dielectric films is solved by means of 4 2 4 characteristic (transfer) matrices. The characteristic matrices are calculated for either w or k taken as gyrotropic (skew symmetric) tensors having off-diagonal elements characterized by the complex, dimensionless, parameterspandq, respectively. Solutions are given for the polar, longitudinal and transverse orientations between the magnetization, the light propagation vector and the reflecting surface. Useful general results include the similarity invariants of characteristic matrices and the precise specification of minimum-equivalent multi-layer structures. A salient feature of magneto-optical scattering is the transfer of energy from two otherwise non-interacting polarization modes, namely modes withHperpendicular or parallel to the incidence plane, respectively. The conversion efficiency (conversivity) depends on two factors: (1) ohmic loss in the magnetic film; (2) conversion matching. Ohmic loss can be reduced by placing the film on the surface of an electric mirror (tangentialE= 0) in an optical standing wave. Conversion matching can be accomplished with dielectric films, somewhat analogous to the case of impedance matching. The need for the concept of conversion matching as distinct from impedance matching can be made clear by considering the general properties of a four terminal-pair (four port) network (junction), of which the magneto-optical scattering problem is an example. Such considerations show that a conversion impedance cannot be defined as a constant characterizing a given magnetic material.