Lecture13 - Chapter 12 Scattering and Absorption by...

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1 1 Chapter 12 Scattering and Absorption by Particles 2 How do we know if Rayleigh Scattering is appropriate for a particular particle? Table 12.1 Chapter 12: Scattering and Absorption by Particles
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2 3 How do we know if Rayleigh Scattering is appropriate for a particular particle? Size vs. Wavelength and Refractive Index λ π r x 2 Size Parameter: r = radius of spherical particle – or of sphere having the same volume or surface area as the particle. λ = wavelength Recall Relative Refractive Index: 1 2 N N m N 2 = Complex refractive index of the particle = n r + i n i N 1 = Complex refractive index of surrounding medium For particles in air, N 1 ~ 1, so m ~ N 2 . N 2 depends on particle composition and λ . | m | ~ Magnitude of N 2 = ( N 2 * N 2 ) 1/2 = ( n r 2 + n i 2 ) 1/2 Typical values in the visible for atmospheric aerosols are n r ~ 1.5 and n i ~ 0.01 (small absorption) to ~1 (e.g., soot). Criterion for Rayleigh Scattering: | m | x << 1 (~0.002-0.2) β i a n 4 = 4 Petty Figure 12.1
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3 5 What happens when radiation encounters a particle that is small compared to the wavelength? The oscillating electric field of the radiation, E , alters the particle’s electron distribution periodically, in phase with E . This charge perturbation is manifested as an oscillating induced dipole moment, p (units = charge × distance, or C m). The ease with which this dipole moment is induced is called the Polarizability , α : ) exp( , 0 t i E E E p ω α r r r r = = The charge acceleration implied by the oscillating induced dipole moment results in scattering of radiation (the induced dipole produces its own oscillating electric field that propagates outward at speed of light). Electric field of the scattered radiation will thus be proportional to the charge acceleration: [ ] ) exp( ) exp( 2 2 2 2 2 t i t t i t p E Scat = r r (where t is time) We’ve said that Rayleigh scattering is proportional to 1/ λ 4 – does this follow? 12.2 6 Electric Vector for Rayleigh Scattering (from last slide) The scattered intensity is proportional to the square of the electric vector: λ π / c 2 , 4 = Scat I Rayleigh scattering is proportional to λ -4 We’ve said that the Rayleigh Phase Function for unpolarized light is given by: ( ) Θ + = Θ 2 cos 1 4 3 ) (cos p Does this follow? CAUTION : Petty changes notation in this chapter so that the incidence direction is now and the scattering direction is ´ !! Define γ as the direction between E o (incident electric vector) and ´ (propagation direction for scattered light). Assume that p (and thus scattered electric vector) is aligned with E o . Intensity of scattered light is proportional to component of scattered electric vector observed in direction ´ , or the projection of E o onto plane perpendicular to ´ . [] ) exp( exp( 2 2 2 2 2 t i t t i t p E Scat = r r
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4 7 E o Incident electric vector is polarized along x axis. γ is angle between Eo & ´.
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Lecture13 - Chapter 12 Scattering and Absorption by...

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