The Milne problem for the temporal correlation function of radiation backscattered from a half space is solved analytically. The angular and temporal dependencies calculated with the Monte Carlo simulations coincide with high precision with the Milne-like solution for a near isotropic scattering; for a highly anisotropic scattering the Monte Carlo results turn to be in a fair agreement with the known measurement, while the Milne-like solution greatly disagree with the experiment. Effects of finite thickness and non-zero absorption are also considered.