We consider the problem of describing steady-state transport of a perpendicularly incident pencil beam of particles through a thin slab of material. The scattering is assumed to be described by the continuous slowing down approximation in energy and by the screened Rutherford formula in angle. For very small screening parameters, it is well known that the scalar flux, as a function of depth and radius, is described reasonably well by the classic Fermi-Eyges formula. However, realistic screening parameters, such as encountered in medical physics applications, are not small enough for this formula, which is Gaussian in radius, to be accurate. A correction to the spatial component of the Fermi-Eyges formula for screened Rutherford scattering is developed. This correction exhibits an algebraic, rather than exponential, falloff of the scalar flux with radius. Comparisons with benchmark Monte Carlo calculations confirm the inaccuracy of the scalar flux spatial distribution of the Fermi-Eyges formula for realistic screening parameters and demonstrate the good results obtained with the present formalism. Contact is made with earlier work by Molière.