Various fairly simple approximations for the scalar flux distribution in an infinite slab with vacuum on both sides and a µn distributed incoming neutron flux at one surface are studied, and the resulting expressions for the outgoing fluxes at the surfaces are compared with Maynard's results in an attempt to find an approximation that will give an error <10% in the outgoing currents for values of c (the number of secondaries per collision) slightly <1 and τ (the optical thickness) up to 5. Of the approximations studied, only a parabolic flux distribution with all components determined from the integral transport equation gave acceptable results.