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However, as the absorptivity / emissivity become significant, additional cross sections are partly blocked by the cross sections already added.— RealClimate
Thus, optical thickness increases linearly with cross section per unit area (equal to cross section per unit volume multiplied by geometric path length), while absorptivity and emissivity 'decay' exponentially to 1 from zero.— RealClimate
Whatever the optical properties are, there is, at any given wavelength, some emissivity and some absorptivity that are the same at local thermodynamic equilibrium. 1 - absorptivity = reflectivity.— RealClimate
After the first reflection or scattering, the intensity I1 = I0* (1-absorptivity) + Ibb*emissivity.— RealClimate
When in local thermodynamic equilibrium, the Second Law requires absorptivity from a direction = emissivity toward a direction, at a location, along the same path, for a given wavelength and polarization.— RealClimate

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