Application of the method of the separation of fluxes to the reflection of light: Calculation of the partial reflection function

In this paper, we continue the investigation of the propagation of radiation in absorbing media using the method of the separation of fluxes. A regular procedure for the calculation of the Green's function is described in the case when the expansion of the scattering phase function in Legendre polynomials involves a finite number of terms. The Green's functions for the isotropic and linear scattering laws are calculated. The partial reflection function and the partial reflection coefficient in an isotropically scattering medium that describe the contribution of those photons in reflected radiation that change the sign of their velocity projection on the z-axis exactly once are analytically calculated. It is shown that the remaining part of reflected radiation, which involves photons that change the sign of their velocity projection on the z-axis three or more times, obeys the well-known cosine law. The results obtained for the partial reflection function and the partial reflection coefficient are compared with the results of calculation using the Chandrasekhar formulas.