Reflection of radiation from an atmosphere with a chaotic magnetic field

We consider a semi-infinite turbulent atmosphere with a chaotic magnetic field. We assume that the ratio of the cyclotron frequency to the radiation frequency is small. In this case the Faraday rotation influences only the radiation polarization. The magnetic-field fluctuations are assumed to be isotropic and of Gaussian type. We present the solution of two problems - the reflection of non-polarized radiation with normal incidence to the surface and the reflection of non-polarized radiation from a point source above the surface. The latter occurs when the observed radiation escapes from the part of the jet where most of the radiation (at the relevant wavelength) arises. In this case the polarization degree depends on the level of magnetic-field fluctuations, the wavelength. and the aperture Theta of the point source, which is determined by the height of the source and the radius of the optically thick part of an accretion disc. The calculations show that the chaotic Faraday rotations very strongly diminish the polarization degree of the emerging radiation compared to the non-magnetized atmosphere. The calculations of the intensity distribution and polarization degree can be used to estimate the level of magnetic-field fluctuations in the accretion discs in active galactic nuclei and binary systems.