RASCAS simulations of the transfer of Lyman-α photons (x_in = 0) emitted at the origin of a uniform plane-parallel slab. Left: mean number of scatterings until escaping the slab as a function of the vertical H I opacity τ_H I. RASCAS runs are shown by black symbols for different assumed gas temperatures (T = 10, 10², 10⁴ K). The red dashed line corresponds to the analytic approximation found by Harrington (1973), N_scatt = 1.612τ_H I. Middle: variation of the emergent spectrum as a function of τ_H I. The solid coloured lines are the results from RASCAS, while the black dashed curves are the analytic predictions of Neufeld (1990). We assume T = 100 K, no recoil effect, and an isotropic angular redistribution. Right: evolution of the Lyman-α escape fraction f_esc as a function of dust optical depth (τ_dust) in the case of a slab with τ_H I = 10⁶ and T = 10² K. The results from RASCAS (filled circles) reproduce very well the analytic prediction of Neufeld (1990) (red dashed line).