It is the purpose of this paper to demonstrate how the matrix operator method can be effectively implemented to couple the radiation fields of the atmosphere and ocean. Azimuthally averaged radiances and irradiances are presented as a function of optical depth for a conservative Rayleigh scattering medium of total optical thickness τmax = 1000 with a dielectric interface placed at optical depths of 0.01, 0.1, 1.0, and 10.0, and for various solar incident angles.