CH4: Reflection and Refraction in a Homogenous Medium.

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

More Details on the Polarization States Elliptical Polarization: The most general representation. Circular Polarization

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

Reflection, Refraction, and Transmission

Radiant Intensity and Flux: How do we deal with reflected radiation? What are examples of each type of reflection?

Another type of reflection without a real interface. 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. Another type of reflection without a real interface. n1sin(1)= n2sin(2) MIRAGES z For a gas, (nr-1) ≈  =gas density. d/dz > 0 for this type or mirage. What does this say about the likelihood of convection?

Snell’s Law: Kinematics

Complex Refractive Index for Water and Ice

Some Basics, Electromagnetic Skin Depth

Wave Penetration Depth in Water and Ice

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.

Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude). i Medium 1 Medium 2 t

Reflectivity of Water And Ice Brewster Angle Mid Visible (green) =0.5 microns nr = 1.339430 ni = 9.243 x 10-10 Microwave =15,000 microns nr = 6.867192 ni = 2.630

Reflectivity of Water And Ice: Normal Incidence What drives the reflectivity?

Rainbow from raindrops 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.

See http://www.philiplaven.com/p8e.html, and atmospheric optics. Rainbow Optics  scattering angle nr See http://www.philiplaven.com/p8e.html, and atmospheric optics.

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.)

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.

Light Scattering Basics (images from Wallace and Hobbs CH4). Angular Distribution of scattered radiation (phase function) x Dipole scattering Sphere, radius r, complex refractive index n=mr + imi mr=1.5 Qs x