Features of the transition radiation (TR) generated in the vacuum ultraviolet range by weakly-relativistic electrons escaping from a target at small (grazing) angles have been theoretically studied. A significant (more than tenfold) increase in the angular density of TR with decreasing escape angle is predicted. It is established that the spectral and angular distribution of the TR intensity significantly depends on the target permittivity and the electron energy and escape angleyesBelgorod State Universit