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Scattering of slow neutrons or x-rays on roughnesses in geometry of total reflection is considered. Part of radiation scattered on roughnesses at the front interface of a plane sample penetrates into the sample and outgoes through its back and edge surfaces. Theory for calculation of angular distribution of transmitted radiation after such a scattering is presented. It is shown that there is a range of angles below the critical one, which does not contain transmitted radiation. If, nevertheless, the radiation is present in this range, it gives information about additional scattering of transmitted radiation on the back surface roughnesses.