Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?

We derive scaling laws for the Rayleigh-Sommerfeld formulation we recently developed to describe light scattering from nanotextured interfaces. These scaling laws provide precious intuition on how to link scattering from different interfaces. In particular, we answer the question how to obtain a Lambertian scatterer into silicon, starting from a Lambertian scatterer into air relevant to the development of light trapping schemes in thin-film silicon solar cells. We also define a Lambertionality factor which measures how close an arbitrary scatterer approaches Lambertian scattering and extend the fundamental 4n2 light trapping limit to arbitrary scattering distributions.