 Polarization of singly scattered sunlight

In ideal single Rayleigh scattering of unpolarized incident light by an isotropic small scatterer, observed intensities perpendicular and parallel to the scattering plane are proportional to 1 and ${\cos }^2\chi$. Their normalized difference is $\mathcal{P}={\sin }^2\chi /(1+{\cos }^2\chi )$. At a right-angle scattering geometry the output is fully linear and perpendicular to that plane. Multiple scattering, large particles and anisotropic scatterers change this ideal sky-polarization law.