Two-dimensional distribution function of polarization fraction p and column density N_H. Top: Ophiuchus field. Bottom: Chamaeleon-Musca field. The distribution functions are presented in logarithmic colour scale and include only points for which p/σ_p> 3. The dashed red lines correspond to the absolute maximum polarization fractions p_max and the solid red curves show the upper and lower envelopes of p as functions of N_H. The solid black line is a linear fit to the decrease of the maximum polarization fraction with column density at the high end of N_H (see Table 2 for the fitting ranges and fit parameters).