INFLUENCE OF SPECULARLY REFLECTING BOUNDARIES ON RADIATION TRAPPING IN A PLANE-PARALLEL SLAB

We consider radiation trapping in a plane-parallel slab with specularly reflecting boundaries. The reflection coefficient of the walls can be different at the two sides of the slab, and may depend on the angle and frequency of the radiation. We derive a closed-form Green's function, and give an efficient method for its evaluation. We show that, in most cases, higher-order modes have practically no influence on the temporal behavior of the emergent radiation when the reflection coefficients at both walls are high, but that they are important when only one wall is highly reflecting. We also investigate the difference between diffuse and specular reflection. For center-of-line opacities k0L exceeding 0.5, the difference in the lowest-order trapping factor is quite small (less than 3% for Doppler line shapes and less than 6% for Lorentzian shapes). Trapping calculations can therefore be simplified by using the formulas for specular instead of diffuse reflection.