pat arnott, atms 749 atmospheric radiation transfer ch4: reflection and refraction in a homogenous...
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Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
CH4: Reflection and Refraction in a Homogenous Medium.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Polarization States: A reminder
Wave/Photon boson: Polarization.
Linear Polarization: E-field in one direction.
Circular, elliptical polarization: E-Efield rotates due to phase difference between horizontal and vertical components.From: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
More Details on the Polarization States
Circular Polarization
Elliptical Polarization:
The most general representation.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Three Choices for Solar Radiation
Emissivity is the same as absorptivity. Source can be visible or infrared radiation, or other wavelengths as well, microwave, etc.
Transmission + Reflection + Absorption = 1
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Reflection, Refraction, and Transmission
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Radiant Intensity and Flux: How do we deal with reflected radiation?
What are examples of each type of reflection?
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Trace velocity matching principle: Snell’s law (continuity of the wavefront at a boundary)
“slow is more normal”Here assume n1=n1r, n1i=0, n2=n2r, n2i=0.
MIRAGES
n1sin(1)= n2sin(2)
For a gas, (nr-1) ≈ =gas density.
d/dz > 0 for this type or mirage.
What does this say about the likelihood of convection?
z
Another type of reflection without a real interface.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Snell’s Law: Kinematics
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Complex Refractive Index for Water and Ice
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Some Basics, Electromagnetic Skin Depth
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Wave Penetration Depth in Water and Ice
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Boundary Conditions at Interfaces: Used with Plane Wave Solutions of Maxwell’s Equations for E and H to get the Fresnel Coefficients.
• Used along with boundary conditions to calculate the single scattering properties of aerosols and hydrometeors (cloud droplets, rain drops, ice crystals, snow flakes, etc), from first principles if possible. {Mie theory for homogeneous spheres, coupled dipole theory for general particles, T-Matrix method, etc}
• Are not used to calculate the radiation field arriving at the surface from the complex atmosphere. Multiple scattering theory is used.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude).
Medium 2
Medium 1
i
t
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Reflectivity of Water And Ice
BrewsterAngle
Microwave =15,000 microns nr = 6.867192 ni = 2.630
Mid Visible (green) =0.5 microns nr = 1.339430 ni = 9.243 x 10-10
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Reflectivity of Water And Ice: Normal Incidence
What drives the reflectivity?
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Geometrical Optics: Interpret Most Atmospheric Optics from Raindrops and lawn sprinklers (from Wallace and Hobbs CH4)
Rainbow from
raindrops
Primary Rainbow Angle: Angle of Minimum Deviation (turning point) for rays incident with 2 chords in raindrops.
Secondary Rainbow Angle: Angle of Minimum Deviation (turning point) for rays incident with 3 chords in raindrops.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Rainbow Optics
scattering angle
See http://www.philiplaven.com/p8e.html, and atmospheric optics.
nr
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Geometrical Optics: Rainbow (from Petty)
Angle of minimum deviation from the forward direction. Focusing or confluence of rays.
x
Distance x is also known as the impact parameter. (Height above the sphere center.)
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Geometrical Optics: Interpret Most Atmospheric Optics from Ice Crystals (from Wallace and Hobbs CH4)
22 deg and 45 deg Halos from cirrus crystals of the column or rosette (combinations of columns) types. Both are angle of deviation phenomena like the rainbow. Crystal orientation important. 22 deg halo, more common, thumb rule to measure size of arc.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Light Scattering Basics (images from Wallace and Hobbs CH4).
Sphere, radius r, complex refractive index n=mr + imi
x
xxLines :
r= x2π
Dimensionless Parameters
SizeParameter≡x=2πr
ScatteringEfficiency≡Qs=σscaπr2
mr=1.5
Qs
Angular Distribution of scattered radiation (phase function)
x x
xDipole scattering