A mixing rule for imaginary parts of refractive indices of aerosols or colloids in the Rayleigh regime

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A Rayleigh mixing rule that relates the effective imaginary part of the refractive index of a composite medium, such as an aerosol or colloid, to the complex refractive index of the Rayleigh particles is derived using Rayleigh scattering theory. The derivation is simple, straightforward, and only weakly dependent on particle morphology. The Rayleigh mixing rule offers an opportunity to derive the imaginary part of refractive index spectra of Rayleigh particles, suspended in a non-absorbing medium with known refractive index spectrum, from an extinction spectrum of the composite medium. However, for this application, the real refractive index spectrum of the particle must be known reasonably well and the imaginary part must be known well enough to decide between two mathematical solutions for it. The Rayleigh mixing rule is compared with widely used mixing rules (i.e., volume, Maxwell Garnett, and Bruggeman mixing rules) and we show that in the small volume fraction regime both the Maxwell Garnet and Bruggeman mixing rules agree with the Rayleigh mixing rule.