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D.K. Lynch, S. Mazuk (The Aerospace Corp.)
The conventional means of quickly determining the scattering regime of a particle is the size parameter X = 2\pi a/\lambda where a is the particle radius and \lambda is the wavelength of light being scattered. As arguments to the Bessell functions in Mie theory, however, X is multiplied by m = Np/N where Np = n +ik is the complex index of the particle and N is the index of the surrounding medium (= 1.0 for a vacuum). The quantity mX is complex (mX = 2\pia/\lambda +i2\pik a/\lambda) For thermal emission from particles, we show that the opacity parameter \Omega = 4\pik a/\lambda= 2kX is a more accurate means of distinguishing between ``small" and ``large" particles. Here ``large" particles emit in a black body-like manner and ``small" particles emit with spectral structure indicative of their optical constants. \Omega is approximately equal to the particle's mean optical depth and is equal to two times the imaginary part of mX. \Omega can be derived from both scattering theory and geometrical optics.
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