Ratio of β over γ plotted against the line optical depth for the approximation in MJ83: Eqs. (3) and (5) with α = 1.5 and Δ = 0 and calculated for τ_c < 5. The approximation is plotted with small squares in the upper panel. The ratio of the exact solution to the assumed approximation is shown in the bottom panel. For each discrete value of τ_i (calculated at 0.025 intervals), the vertical lines indicate the range in the continuum optical depth, from 0 (largest value of β/γ) to the maximum value (lowest value). The small vertical lines at the bottom of the upper panel and at the top of the bottom panel indicate the optical depth where the difference between the exact calculation and the approximation is largest.