Particle optics in the Rayleigh regime.

Light scattering and absorption by particles suspended in the atmosphere modifies the transfer of solar energy in the atmosphere, thereby influencing global and regional climate change and atmospheric visibility. Of particular interest are the optical properties of particles in the Rayleigh regime, where particles are small compared with the wavelength of the scattered or absorbed light, because these particles experience little gravitational settlement and may have long atmospheric lifetimes. Optical properties of particles in the Rayleigh regime are commonly derived from electromagnetic theory using Maxwell's equations and appropriate boundary conditions. The size dependence of particle scattering and absorption are derived here from the most basic principles for coherent processes such as Rayleigh scattering (i.e., add amplitudes if in phase) and incoherent processes such as absorption (i.e., add cross sections), at the same time yielding understanding of the upper particle size limit for the Rayleigh regime. The wavelength dependence of Rayleigh scattering and absorption are also obtained by adding a basic scale invariance for particle optics. Simple consequences for particle single-scattering albedo ("whiteness") and the optical measurement of particle mass densities are explained. These alternative derivations complement the conventional understanding obtained from electromagnetic theory.