Abstract

It is generally accepted that, for a single sphere, the Lorenz-Mie efficiency factor for extinction Q_e approaches 2 as the size parameter of the sphere X approaches infinity. We show that, for an ensemble of lognormally distributed spherical particles, the dimensionless extinction coefficient assumes a simple mathematical form when the particle-size distribution is dominated by particles for which Q_e → 2. The accuracy with which this asymptotic expression for the dimensionless extinction coefficient approaches an exact Lorenz–Mie calculation is examined when the complex refractive index is given by 1.10 ≤ n ≤ 3.00 and 0.0 ≤ k ≤ 4.0 and when the parameters of the lognormal particle-size distributions are given by mass median size parameters 0.01 ≤ X_m ≤ 100.0 and geometric standard deviations 1.1 ≤ σ_g ≤ 3.0.

© 1984 Optical Society of America

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