Multidimensional semi-analytical benchmarks to provide highly accurate standards to assess routine numerical particle transport algorithms are few and far between. Because of the well-established 1D theory for the analytical solution of the transport equation, it is sometimes possible to "bootstrap" a 1D solution to generate a more comprehensive solution representation. Here, we consider the searchlight problem (SLP) as a multidimensional benchmark. A variation of the usual SLP is the interior beam SLP (IBSLP) where a beam source lies beneath the surface of a half space and emits directly towards the free surface. We consider the establishment of a new semi-analytical benchmark based on a new FN formulation. This problem is important in radiative transfer experimental analysis to determine cloud absorption and scattering properties.