tokens: μ) and Q 0 (0, μ) in the case of ( 1 7 ) are simple: In Table 1 we give the angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and the degree of polarization p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent at and 1 for the incident non-polarized radiation perpendicular to the surface. Note that negative Q 0 (0, μ) corresponds to the wave electric-field oscillations perpendicular to the plane ( nN ). This holds in our case. Table 1 shows that the chaotic Faraday rotations strongly decrease the polarization and weakly affect the angular distribution. Table 1. The angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and the degree of polarization p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent at and 1 for the incident non-polarized radiation normal to the surface. Recall that we consider the atmosphere without pure absorption (a conservative atmosphere). It follows from equation ( 13 ) that the zero moments of functions β(μ) and γ(μ) are equal to and , respectively. These moments are μ-integrals over the interval (0,1) (see Silant’ev et al. 2019 ). Taking the integral μ I 0 (0, μ) dμ over the same interval and using equation ( 13 ), we obtain that the flux of outgoing radiation is equal to the flux F I of the incident radiation. For a conservative atmosphere this is the evident result. In Fig. 1 the polarization degree p (μ) of the reflected radiation for different parameters h is given. The angular dependence J (μ) practically does not depend on h . Therefore, we give J (μ) for and 30. The numbers over the curves denote the values of h . Figure 1. The angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and polarization degree p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent of reflected radiation. The incident radiation is perpendicular to the surface. The numbers denote the values of parameter h . It is of interest to compare the multiple scattered outgoing intensity I 0 and parameter Q 0 to the results for single scattered radiation: The flux of outgoing single scattered radiation is equal to F single = 0.168 F I , i.e. only ≃ 17 per cent of the total flux. The other 83 per cent of the emerging radiation is concerned with two and more scatterings in the semi-infinite atmosphere. In our case, the considered normal incident radiation penetrates deeper into the atmosphere than in other inclinations. It means that F single = 0.168 F I is the minimum value of the single scattered radiation fluxes. The corresponding angular distribution and the degree of polarization have the form The polarization p single (μ) at μ = 0 is equal to 100/(1 + h ) per cent. This result clearly demonstrates the decrease of polarization with increasing parameter h . This decrease holds along the outflow of single scattered non-polarized radiation. Recall that single scattering of non-polarized radiation gives rise to 100 per cent polarization of the scattered one if the scattering angle (the angle between the incident radiation and the scattered one) is equal to 90° (see, for example,
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