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Applied Optics

Applied Optics


  • Vol. 38, Iss. 24 — Aug. 20, 1999
  • pp: 5229–5231

Size parameter for thermally emitting particles

David K. Lynch and Stephan Mazuk  »View Author Affiliations

Applied Optics, Vol. 38, Issue 24, pp. 5229-5231 (1999)

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For thermal emission from particles the conventional size parameter X = 2πa/λ does not distinguish between small and large particles. We show that the opacity parameter Ω = 4πka/λ = 2kX is a more accurate means of demarcating the two emission regimes. Ω is approximately equal to the particle’s mean optical depth, and it can be derived from both scattering theory and geometrical optics.

© 1999 Optical Society of America

OCIS Codes
(290.2200) Scattering : Extinction
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles

Original Manuscript: March 2, 1999
Revised Manuscript: May 21, 1999
Published: August 20, 1999

David K. Lynch and Stephan Mazuk, "Size parameter for thermally emitting particles," Appl. Opt. 38, 5229-5231 (1999)

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. Irradiance F from a particle is proportional to emissivity × Planck function = Qabs *Bλ(T). For a blackbody, Qabs is unity. When Qabs ≪ 1, F shows a spectral structure that indicates its optical constants, which in turn are determined by the chemical composition and crystalline state. When Qabs ≈ 1 as it does when the particle is large, the emission is broad and featureless with only a single maximum whose width is about the same as that of the Planck function. Although there may be minor deviations of Qabs from unity that disqualifies it from being a true blackbody, the radiation is nonetheless roughly Planckian and entirely different from when Qabs ≪ 1.
  4. T. Henning, B. Begemann, H. Mutschke, J. Dorschner, “Optical properties of oxide dust grains,” Astron. Astrophys. Suppl. 112, 143–149 (1995).

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