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**Rayleigh and Mie Scattering**

Remote Sensing ERAU Dr. Darrel Smith September 30, 2008

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**Rayleigh & Mie Scattering**

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Rayleigh Scattering

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**Rayleigh Scattering Light scattering off of air molecules (N2, O2)**

Can be extended to scattering from particles up to ~ 1/10 . Rayleigh scattering off the molecules of the air gives rise to a “blue” sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much smaller than the wavelength to be:

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Rayleigh Scattering

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**Rayleigh Scattering from Particles**

When scattering from a particle of size d with light of wavelength , the Rayleigh scattering is found to be: where R is the distance to the particle, n is the index of refraction, and is the scattering angle.

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Cross Section The cross-section of a particle is determined by the following equation where: is the differential cross section. Another way of representing this is by:

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Problem Find the Rayleigh scattering cross-section for scattering from a small particle of size d using a wavelength if the scattered intensity is: where R is the distance to the particle, n is the index of refraction, and is the scattering angle. Answer:

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**Scattering from molecules**

A 5 mW green laser pointer is visible at night due to Rayleigh scattering and airborne dust. = 532 nm

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Homework Problem #1 If the Rayleigh cross-section for an N2 molecule is 5.1 x m2 at a wavelength of 532 nm (green light), what would be the characteristic size of an N2 molecule? Assume that the index of refraction of air is: nair =

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Problem What is the number density nbeam for a 5 mW green laser pointer whose wavelength is 532 nm and whose cross-sectional beam size is 2 mm?

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Homework Problem #2 What fraction of the light from a 532 nm pen laser gets scattered every meter?

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**Degree of Polarization**

In general, Rayleigh scattering is for randomly polarized incident flux and the scattered flux will be polarized. The degree of polarization induced by scattering from a small particle exposed to randomly polarized flux is: Bohren and Huffman (1998)

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Homework Problem #3 Plot the “degree of polarization” as a function of scattering angle . At what angle is the scattered light completely polarized? How might you observe this?

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