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Opaque Minerals

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Geometry of Fresnel, normal incidence. In our case, n2=1 and k2=0 ... Fresnel Reflectance at normal incidence for thick layer (d 'big') In vacuum or air, n0=1 ... – PowerPoint PPT presentation

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Title: Opaque Minerals


1
Opaque Minerals
  • Lecture 4

2
Important Opaques
  • Moon ilmenite (FeTi03),chromite
  • Asteroids troilite (FeS), carbon (C )
  • Mars magnetite (Fe3O4)
  • Dark minerals, with weak spectral features

3
Odd behavior of opaques (normal in thermal
infrared)
  • Pyrite (FeS2)
  • Fine particles darker than larger particles
    (better emitters)
  • From Geochemical Analysis, Pieters and Englert

4
More oddity
  • Troilite (FeS)
  • From BE Clark, Spectral mixing of S-type
    asteroids, JGR 100 e7, p14443 1995
  • Note smaller sizes are brighter

5
  • For transparent particles, single scattering
    albedo increases with decreasing grain size.
  • For absorbing particles, single scattering albedo
    must decrease with decreasing grain size
  • Volume vs. surface scattering
  • Nice words, but doesnt address the question

6
Back of the envelope…
  • Paradoxically, highly absorbing materials are
    also highly reflective (e.g metal)
  • Why would reducing the grain size decrease the
    single scattering albedo?
  • Why would volume scattering decrease the
    albedo?
  • R(thick) gt R(thin)T(thin) must be true

7
Geometry of Fresnel, normal incidence
In our case, n21 and k20
8
n and k and complex numbers
  • n and k are the complex indices of refraction
  • nnik
  • When k is small (lt1/1000), absorption is weak and
    n governs the angle of refraction at boundaries
    between media (Snells Law), and k governs
    absorbance
  • When k is comparable to n, then n has little to
    do with refraction, both are highly coupled
  • n is complex only for mathematical convenience.
    Complex mathematics make describing the behavior
    of harmonic oscillators (like light)more
    convenient (for somebody).
  • n and k are simply parameters describing the
    behavior of harmonic oscillators. Light behaves
    like a harmonic oscillator.

9
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10
Fresnel Reflectance at normal incidence for thick
layer (d big)
In vacuum or air, n01 p,s subscript refers to
polarization state If k approx equal to n, R is
about 1.
11
Reflectance and transmission of thin absorbing
films
n21
12
The necessarys
For thin film in air, n0,21, k0,20
13
Problem
  • If these equations are correct, for absorbing
    particles, RthinTthin lt Rthick
  • In other words, the single scattering albedo goes
    down when d decreases because the sum of
    reflectance and transmission are less than for a
    thick particle

14
The homework problem
  • Show RT as a function of d, where d is in the
    range from 10nm to 100 microns
  • How does RT compare to R for a thick medium?
  • Sanity check RT should equal R thick, when d
    is big.
  • Note because of the trig terms, the answer will
    oscillate as a function of d. Also d is in same
    units as wavelength (see defs of alpha and gamma)

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