Transcript Rayleigh and Mie Scattering

Rayleigh and Mie Scattering
Remote Sensing
ERAU
Dr. Darrel Smith
September 30, 2008
Rayleigh & Mie Scattering
Rayleigh Scattering
Rayleigh Scattering
1. Light scattering off of air molecules (N2, O2)
2. Can be extended to scattering from particles up to
~ 1/10 .
3. Rayleigh scattering off the molecules of the air gives
rise to a “blue” sky.
4. Lord Rayleigh calculated the scattered intensity from
dipole scatterers much smaller than the wavelength
to be:
Rayleigh Scattering
Rayleigh Scattering from Particles
1. When scattering from a particle of size d with
light of wavelength , the Rayleigh scattering
is found to be:
2. where R is the distance to the particle, n is
the index of refraction, and  is the scattering
angle.
Cross Section
1. The cross-section of a particle is determined
by the following equation
where:
is the differential cross section.
2. Another way of representing this is by:
Problem
1. Find the Rayleigh scattering cross-section for
scattering from a small particle of size d
using a wavelength  if the scattered intensity
is:
2. where R is the distance to the particle, n is
the index of refraction, and  is the scattering
angle.
Answer:
Scattering from molecules
A 5 mW green laser pointer is
visible at night due to Rayleigh
scattering and airborne dust.
 = 532 nm
Homework Problem #1
1. If the Rayleigh cross-section for an N2
molecule is 5.1 x 10-31 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 = 1.000293
Problem
1. 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?
Homework Problem #2
1. What fraction of the light from a 532 nm pen
laser gets scattered every meter?
Degree of Polarization
1. In general, Rayleigh scattering is for randomly
polarized incident flux and the scattered flux
will be polarized.
2. The degree of polarization induced by scattering
from a small particle exposed to randomly
polarized flux is:
Bohren and Huffman (1998)
Homework Problem #3
1. Plot the “degree of polarization” as a function of
scattering angle .
2. At what angle is the scattered light completely
polarized?
3. How might you observe this?