Robin Hogan

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Estimating cloud particle size usingthe moon

• Robin Hogan

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What causes the coloured rings around the moon?

• Huygens principle states that any part of a
  wave front can be treated as its own source of
  spherical waves.
• This predicts that light (and many other types of
  wave) will diffract around an obstacle (e.g.
  cloud particles)
• A wave front Maxwells interpretation of this
  is the point of maximum electric field

Direction of incidence of electromagnetic
radiation
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Superposition principle


Scattering amplitude from an obstacle (including
unscattered radiation)
Scattering amplitude from the equivalent hole
Original plane wave

• From this we deduce that
• The scattering amplitude of the obstacle (NOT
  including unscattered radiation) is the negative
  of the scattering amplitude from the equivalent
  hole
• But intensity amplitude squared!
• Babinets principle the pattern of scattered
  intensity from an obstacle is the same as that
  from the equivalent hole

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Fraunhofer diffraction

• The scattering pattern from a hole is easier to
  calculate than a particle
• The first minimum occurs when light from opposite
  sides of hole destructively interferes
• Occurs when the distance travelled differs by
  half a wavelength
• The scattering pattern will be broader for
• Smaller holes (i.e. particles with smaller radius
  r)
• Longer wavelengths l

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What about the colours?

• Red light has a longer wavelength, so forms a
  broader pattern and the characteristic red ring
• Ring radius 2 -gt particle radius r9 mm
• Ring radius 3.5 -gt particle radius r5 mm
• Ring radius 7 -gt particle radius r2.5 mm
• For reference, note that the sun and moon both
  have an angular diameter in the sky of 0.5
• The effect is known variously as
• Corona
• Aureole
• Iridescence

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How well do the predicted colours match the
observations?

• Droplets must be nearly all the same size so that
  the colours dont wash out

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Estimating particle size
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Examples with the sun
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Bishops ring

• Produced by stratospheric aerosol, usually from a
  volcano
• First exact description of the associated corona
  was after the Krakatoa volcano on August 27, 1883
• Sereno Bishop observed it on September 5, 1883 in
  Honolulu
• Let me draw your special attention to the very
  strange corona or halo that extends about 20 to
  30 degrees away from the sun. It could be seen
  here every day, and the whole day long. A whitish
  veil with a shade of pink and violet or purple
  shadow in front of the blue background. I dont
  know any other report on such a corona. It is a
  hardly remarkable object.
• This corresponds to particles of around 1-2
  micron in size

The Scream (Munch 1893) shows Krakatoa-induced
red skies?
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Bishops ring after Pinatubo in 1991

• Photo taken in Finland in May 1992

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Texas aureole from Saharan dust?