4 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:
6 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.
7 Cross SectionThe cross-section of a particle is determined by the following equation where: is the differential cross section.Another way of representing this is by:
8 ProblemFind 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:
9 Scattering from molecules A 5 mW green laser pointer is visible at night due to Rayleigh scattering and airborne dust. = 532 nm
10 Homework Problem #1If 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 =
11 ProblemWhat 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?
12 Homework Problem #2What fraction of the light from a 532 nm pen laser gets scattered every meter?
13 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)
14 Homework Problem #3Plot the “degree of polarization” as a function of scattering angle .At what angle is the scattered light completely polarized?How might you observe this?