The recently developed FN method is used to solve the half-space albedo problem and the half-space constant-source problem. In addition, the reflected and transmitted currents for the finite slab and the critical thickness of a multiplying slab are reported. As further tests of the method, the inverse problem for the finite slab is solved, and the flux distortion factor for typical two-media problems is computed. It is shown that the FN method, although particularly concise, yields excellent numerical results for the problems considered.