As Fig. A.1, but for λ = 1500−11 000 Å. The impact of the frequency derivative (turquoise versus black) is clearly visible. Without inclusion, no smooth transition between detailed and approximate treatment (at λ_max = 10 000 Å) would be possible. Setting I⁻ to zero at all frequencies (red curve in Fig. A.1) results in a flux-distribution identical to the black one in the optical range, whereas specifying I⁻ ≠ 0 only for optically thick lines and continua, and neglecting the frequency gradient (dark blue curve in Fig. A.1), results in fluxes similar to the turquoise ones.