1Scattering fundamentals Scattering can be broadly defined as the redirection of radiation out of the original direction of propagation, usually due to interactions with molecules and particles Reflection, refraction, diffraction etc. are actually all just forms of scattering Matter is composed of discrete electrical charges (atoms and molecules dipoles) Light is an oscillating EM field excites charges, which radiate EM waves These radiated EM waves are scattered waves, excited by a source external to the scatterer The superposition of incident and scattered EM waves is what is observed

2Types of scattering

Elastic scattering the wavelength (frequency) of the scattered light is the same as the incident light (Rayleigh and Mie scattering)

Inelastic scattering the emitted radiation has a wavelength different from that of the incident radiation (Raman scattering, fluorescence)

Quasi-elastic scattering the wavelength (frequency) of the scattered light shifts (e.g., in moving matter due to Doppler effects)

3Parameters governing scattering (1) The wavelength () of the incident radiation

(2) The size of the scattering particle, usually expressed as the non-dimensional size parameter, x:

r is the radius of a spherical particle, is wavelength

(3) The particle optical properties relative to the surrounding medium: the complex refractive index

Scattering regimes:

x >1 : Geometric scattering

x =2pir

4Light scattering 1. Rayleigh scattering

Rayleigh scattering is the elastic scattering of light by molecules and particulate matter much smaller than the wavelength of the incident light. It occurs when light penetrates gaseous, liquid, or solid phases of matter. Rayleigh scattering can be considered to be elastic scattering since the photon energies of the scattered photons is not changed.Rayleigh scattering is a process in which electromagnetic radiation is scattered by a small

spherical volume of variant refractive index, such as a particle, bubble, droplet, or even a density fluctuation. In order for Rayleigh's model to apply, the sphere must be much smaller in diameter than the wavelength () of the scattered wave; typically the upper limit is taken to be about 1/10the wavelength.

Why is the Sky Blue?

5The strong wavelength dependence of the scattering (~ 1/4) means that shorter (blue) wavelengths are scattered more strongly than longer (red) wavelengths. This results in the indirect blue light coming from all regions of the sky.

Light scattering 1. Rayleigh scattering

is the scattering angle

6Light scattering 1. Rayleigh scattering

Atmospheric polarization is a direct result of the Rayleigh scattering of sunlight by gas molecules in the atmosphere. Upon impact between a photon from the sun and a gas molecule, the electric field from the photon induces a vibration and subsequent re-radiation of polarized light from the molecule. The radiated light is scattered at right angles to the direction of sunlight propagation, and is polarized either vertically or horizontally, depending upon the direction of scatter. A majority of the polarized light impacting the Earth is polarized horizontally (over 50 percent), a fact that can be confirmed by viewing the sky through a polarizing filter.

Scattered blue light is polarized. The picture on the right is shot through a polarizing filter which removes light that is linearly polarized in a specific direction.

7Light scattering 2. Mie scattering

The scattering from molecules and very tiny particles (< 1 /10 wavelength) is predominantly Rayleigh scattering. For particle sizes comparable with a wavelength, Mie scattering predominates. This scattering produces a pattern like an antenna lobe, with a sharper and more intense forward lobe for larger particles. Miescattering can be considered to be elastic scattering.

8Light scattering 2. Mie scattering

Mie scattering white clouds, fog, Lunar halo - an exact solution for homogeneous spherical particles.

Type of particles: dust, smoke, soot, volcanic ash, water vapor, polen

Partical size

Scattering intensity 41/I to 0

Mean diameter 0.1 to 10m

9Light scattering 3. Non-selective scattering or geometrical scattering

Rainbow: for large particles - x = 10,0000 Primary rainbow: single internal reflectionSecondary rainbow: double internal reflection

Rainbows: angular relationships predicted from geometric optics and ray tracing (using Snels Law)

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Rayleigh: d

Light scattering 3. Non-selective scattering or geometrical scattering

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Light scattering regimes

There are many regimes of particle scattering, depending on the particle size, the light wave-length, and the refractive index.

This plot considers only single scattering by spheres. Multiple scattering and scattering by non-spherical objects can get really complex!

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