Effective Extinction curves (left hand figure) and reddening curves around the extinction bump (right hand figure) for a turbulent distant screen. The intrinsic extinction curves with and without extinction bump are shown as dashed-dotted and as dashed curve, respectively. The effective extinction and reddening curves without and with change of the dust properties as function of optical depth are shown either as dotted curve or solid curves. Added is also the mean extinction curve for the limit of a non turbulent screen (grey curve). It is assumed that the extinction bump at 2175   Å is absent below a column density N_H = 10²¹   cm^-2 which corresponds, assuming R_V = 3.1 (Fitzpatrick 1999) and a dust-to-gas-ratio of N_H/E(B − V) = 5.8  ×  10²¹   cm^-2 (Bohlin et al. 1978), to A_V ≈ 0.53   mag. The curves are labelled with the corresponding standard deviation σ_lnξ of the log-normal density distribution of the normalized column density ξ = N_H/ ⟨ N_H ⟩ .