Extinction paradox

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In the small wavelength limit, the total scattering cross-section of an impenetrable sphere is twice its geometrical cross-sectional area (which is the value obtained in classical mechanics).[1]

Several explanations for this phenomenon have been proposed:[2]

  • destructive interference inside particle shadow[3]
  • diffraction and shadowing of light by particle[4]
  • incident wave must be cancelled inside particle[5]
  • Superposition of incident and scattered field[6]


  1. ^ Newton, Roger G. (2002). Scattering Theory of Waves and Particles, second edition. Dover Publications. p. 68. ISBN 0-486-42535-5. 
  2. ^ "TPDSci Ind Ext". tpdsci.com. Retrieved 2014-02-28. 
  3. ^ Brillouin, L. (1949). "The Scattering Cross Section of Spheres for Electromagnetic Waves". Journal of Applied Physics. 20 (11): 1110. doi:10.1063/1.1698280. 
  4. ^ Light Scattering by Small Particles. ISBN 9780486642284. OCLC 264445223. 
  5. ^ Berg, M. J.; Sorensen, C. M.; Chakrabarti, A. (2011). "A new explanation of the extinction paradox". Journal of Quantitative Spectroscopy and Radiative Transfer. 112 (7): 1170. doi:10.1016/j.jqsrt.2010.08.024. , open access at DigitalCommons here
  6. ^ Lai, H. M.; Wong, W. Y.; Wong, W. H. (2004). "Extinction paradox and actual power scattered in light beam scattering: A two-dimensional study". Journal of the Optical Society of America A. 21 (12): 2324. doi:10.1364/JOSAA.21.002324.