Left: radial profiles of the degree of polarisation due to scattering of a protoplanetary disk seen face-on for different wavelengths λ (reference model). The intensity includes both direct and scattered thermal radiation. The shaded areas show the radial distance where the optical depth through the disk to the observer is in the range between 0.1 and 0.02. Right: analytical polarisation degree of a single scattering event p = − S₁₂ ∕S₁₁ for the wavelengths λ = 350 μm (solid lines) and λ = 2 mm (dashed lines), averaged over the entire grain size range from 5 nm to 1 mm for different values of the exponent q of the grain size distribution.