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Atmospheric Optics
Great Web Sites: Les Cowley
Claudia Hinz:
Finnish Halo Blog:
The Phenomena
Are Produced by
Crepuscular Rays
Scattering and Perspective
Sky and Sun Colors
Scattering and Absorption
Refraction and/or Reflection
Refraction and Reflection
Coronas and Iridescence
Oil Slicks
All atmospheric optical phenomena are produced when the path of light is
obstructed. This can happen in several ways. Light is…
Scattered (splattered) in all directions when it passes microscopic aerosol
particles or air molecules.
Reflected (bounced) from the surface of large particles such as raindrops and
ice crystals.
Refracted (bent) gradually as it travels through the atmosphere, or abruptly as
it passes between water and air.
Diffracted into a field of patterned waves as it skirts around tiny cloud droplets.
Absorbed by matter and extinguished.
Optical phenomena are colored when the obstruction of light varies with
Rainbows, Halos
Rainbows, Halos
Rays, Sky Light
and Color, Glories
The Green Flash and Chinese Lantern Effect
Pekka Parviainen
This is a form of mirage caused by a combination of unusually large refraction
and Rayleigh scattering (preferential scattering of short light waves by tiny
particles) when temperature increases in a narrow height range of height above
a cold surface (a near-surface temperature inversion).
Change of direction of the light path (bending) when one part of a wave
crest or trough moves faster than another. For light, this occurs when light
moves obliquely from one medium (air) to another (water) or when the
density of the medium varies.
Spectral colors appear when light passes through a prism because each
wavelength is refracted by a different angle. This is called dispersion.
Natural substance with
the largest refraction
and largest dispersion?
Waves always bend
toward the region where
they move slowest. Red
is usually refracted or
bent least of all colors
Enrique Hita Villaverde Facultad de Ciencias – Universidad de Granada
Superior Mirage – Victoria, British Columbia, Canada
In this photo, air near the ground is much colder and denser than the warmer air above so light
waves travel slower. When the light waves pass through the temperature inversion, they speed up
and are refracted or bent downwards. Looking up, we actually see light coming from below.
When air near the ground is much warmer and less dense than colder air above, light waves near
the ground travels faster than light waves above and thus are refracted or bent upwards. Looking
down on hot, dry ground, we actually see shimmering skylight above that appears like water.
The Superior Mirage
When temperature increases with height, inverted and possibly
magnified images of objects appear higher than in reality because
light waves are bent down as they pass through elevated inversions.
Sometimes called Fata Morgana, superior mirages
are common in the Arctic and have fooled explorers,
who named islands that never existed.
And make the
image appear
up in the sky
Light Beams Bend in
the Elevated Inversion
Light beams below the
inversion do not bend
1. Rays bend toward region where waves move slowest (where air is cold)
2. Rays bend most where temperature gradient is the largest
Crepuscular Rays (Divine Rays)
Caspar David Friedrich Tetschen Altar or Cross in the Mountains 1807-08
Crepuscular rays are
produced when light is
scattered by aerosols.
Crepuscular Rays
Crepuscular Rays
are sunbeams illuminated by light scattered toward the viewer by
aerosols and air molecules. They appear by contrast with the
surrounding shaded air.
The closer the crepuscular ray to the observer, the wider it appears.
But since sun rays are parallel, the apparent spreading results from
linear perspective.
Crepuscular rays generated by laser light passing through artificial
fog. Compliments of Michael Vollmer
Light and Colors
of the Sky
Preferential scattering
of short waves makes
the sky blue.
But note that the sky is
whiter near the horizon
Why is the Sky Blue?
Skylight is sunlight that has been scattered in all directions by air
molecules and aerosol particles. The sky is usually blue because
particles such as air molecules that are much smaller than the
wavelength scatter short waves much more efficiently than long waves,
just as our bodies reflect the ripples that strike it in the bathtub but have
no effect on ocean waves that pass us on their way to shore. This is
called Rayleigh Scattering after Lord Rayleigh who proved that the
amount of scattering by tiny particles varies inversely with the 4th power
of the wavelength. Thus, air molecules scatter the shortest violet waves
[7/4]4  10 times more efficiently than the longest red waves.
Even though violet light is scattered most efficiently, the Sky is blue
and not violet because air molecules scatter significant amounts of
blue and green light, and progressively smaller amounts of yellow,
orange, and red light. Under normal daytime conditions, the mixture of
skylight averages out to a pale blue that whitens toward the horizon.
Aerosol particles are larger than air molecules and scatter the
different wavelengths of light less selectively and by smaller angles. This
makes hazy skies whiter and brighter, especially near the sun.
Pure Air
Hazy Air
Aerosols whiten and brighten the sky around
the Chariot of the Sun God, Apollo (Madrid)
The Sun’s and Sky’s Coat of Many Colors
Skylight is sunlight that has been scattered in all directions. Sunlight is direct
light that penetrates the atmosphere without being scattered. Outside the
atmosphere, direct sunlight is white. At ground level, the Sun is slightly yellow when it is
high in the sky and the sky is blue because  30% of the shortest violet waves and only
 3% of the longest red waves have been scattered. But as the Sun nears the horizon it
must penetrate almost 40 times as much air through the wafer-thin atmosphere to reach
the ground as when it is overhead! Then  99.9999% of the violet and blue waves, and 
70% of the longest red waves have been scattered out of the sunbeam, so the Sun turns
red or orange. The lower the Sun in the sky the longer its path through the wafer
thin atmosphere so more light waves (especially short waves) get scattered and
less penetrate. Thus, the more air a light beam penetrates, the redder it gets.
V = 0%
R = 30%
V = 70%
R = 97%
% of light that penetrates the atmosphere. Most
violet and almost all red light penetrate when
the Sun is overhead but virtually no violet
penetrates when the Sun lies on the horizon.
Post Volcanic Crimson Twilights and Blue Moons
At twilight, when the troposphere lies in the shadow of night, the stratosphere is sunlit. Major forest fires and large
volcanic eruptions produce crimson twilights because they inject the stratosphere with enormous numbers of
aerosol particles and sulfurous droplets 1 to 2 m in diameter that scatter long waves (red) more than short
waves. These particles also turn the Sun or Moon blue because they allow the shorter, blue waves to penetrate
further. But that only happens “once in a blue moon”. Crimson twilight skies last a few months to a few years after
major eruptions. Slowly the particles fall out of the stratosphere and are rapidly washed to the ground by rain or
snow. But while they remain in the stratosphere they cool Earth’s climate.
Claude’s Fantastic Sunset Paintings made Turner Jealous
Until Tambora blew in 1815 and produced fantastic twilight skies
HALOS – Celestial Circles: Aerial Arcs
22 Halo
Halos are produced when sunlight is refracted and/or
reflected by ice crystals. The 22 halo is one of many halos.
Features of the halos are determined by 5 factors, 1: crystal
shape, 2: crystal orientation, 3: light path through or on the
crystals, 4: Sun’s height in the sky, 4: cloud optical thickness.
The 22° Halo and the Path of Light through the Ice Crystals
The 22 halo is a circular ring of light whose inside appears 22 from the Sun or
Moon. The inside is reddish because red light is refracted least of all the colors of
the spectrum. It is one of the most common halos but its colors are washed out.
The halo is the classic warning sign of an approaching winter storm.
Crystal Form – Usually a Column
Light enters a rectangular
face and exits an alternate
(not opposite or adjacent)
rectangular face
To produce the 22° halo, crystals must be randomly oriented to bend sunbeams up,
down, left, right, and diagonal and form a complete circle around the Sun or Moon.
Many different halos are possible. In the next
slide the tangent arc at the top of the 22º halo
forms when pencil crystals fall with their long
axes horizontal so that light refracted by
alternate rectangular faces is bent mainly up
or down. The sundogs at the sides of the
halo form when plate
crystals fall horizontally
(with rectangular faces
vertical) so that light
refracted by alternate
rectangular faces is bent
either right or left. Les Cowley’s Fantastic website
22 halo with Sundogs to left and
right, sun pillar and upper tangent
arc above. Bright spots are light
from individual nearby crystals
Path of Light for the 46° Halo
The 46 halo is a circular ring of light whose inside appears 46 from the Sun or Moon. It
is seldom seen and even at its best, is never as bright as the 22 halo. However, the
circumzenithal and circumhorizontal arcs that are produced when light takes this path
through horizontal plate crystals can be extremely bright and have vivid spectral colors.
Crystal Form – Usually a Thick Plate
Light enters a rectangular
face and exits a hexagonal
face (or vice-versa).
Circumhorizontal Arc
The circumhorizontal arc forms parallel to the horizon at least 46 below the Sun when
the Sun is at least 58 above the horizon. The colors are purest when the Sun is 68
above the horizon. It is produced when light enters a vertically oriented rectangular
side of a plate crystal and exits the bottom, hexagonal face. Since it is only produced
when the Sun is high in the sky it can only be seen near noon at any season in the
tropics or around the summer solstice in the mid latitudes, but never near the Poles.
I. Halos and the Forms of Crystals
Simple crystals such as plates and
columns produce the brightest and
most spectacular halos.
Most crystals have a complex form
with many facets that confuse the light
and produce weak halos.
The simple crystals above left were collected during the South Pole Halo Display that
includes the 22º halo, the parhelia (sun dogs), parhelic circle, upper tangent arc and
Parry arc to the 22º halo, the infralateral and supralateral arcs to the 46º halo and the
spectral circumzenithal arc.
The Clustered and Rimed Crystals below are so complex
that they cannot Produce Halos
South Pole Halo Display
Jarmo Moilanen
II. Halos and the Number of Crystals
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* * * **** *** ***** ***** * ** * * *
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22° 22°
Cloud Thickness
The fraction of light that penetrates a medium without being
scattered or absorbed is equal to e-t where t is called the optical
thickness. The brightest halos are produced by clouds with
optical thickness between about 0.04 and 2. Optically thinner
clouds have too few crystals to refract much sunlight while clouds
that are optically thicker scatter the sunlight so many times before
it can emerge that the result is an incoherent gray color.
At t = 1 (t = 2), only 1/e  36.8% (1/e2  13.5%) of the light penetrates the cloud without being
scattered. When t < 0.02 a cloud is optically too thin to see, but because ice crystals focus light,
halos may be visible. When t > 10 the Sun cannot be seen.
Impact of Cloud Thickness on Halo Brightness
Cloud Thin –
Sun Strong,
Sky Blue and
Halo Weak
Sky Pale,
Halo Bright
Thick Cloud
– Sun Weak,
Sky Gray,
Halo Weak
Rainbows, coronas, and glories are
produced when sunlight strikes drops
Rainbows, Coronas and Glories and Cloud
Droplets and Raindrops
Bright, vividly colored rainbows are produced when sunlight strikes raindrops
between 0.1 and 2 mm in diameter because such drops are spherical and
geometric optics applies. Larger drops flatten and oscillate. Smaller droplets
do not refract light well but scatter or diffract it in more complex ways, and
produce white fog or cloud bows and glories opposite the sun (around an
observer’s shadow) or coronas and iridescent clouds around the sun.
Sun Beam
Sunlight strikes everywhere on the drop but
only the ‘chosen’ point leads to the rainbow
Refraction #1
Reflection #1
Refraction #2
Enrique Hita Villaverde Facultad de Ciencias – Universidad de Granada
The Optics of the Rainbow
is similar to the Optics of
the Eye because Raindrops
and Eyeballs are spheres.
Right eye (horizontal cross section)
Visual Axis
Light can only enter the
eye through the pupil.
Effective Pupil of Drop
Raindrops don’t have pupils
but the rays that produce the
bow strike the drop only in a
narrow zone.
Descartes’ Illustration
of the Rainbows
A swath of many drops is
needed to make a rainbow.
The next slides show how the
number of drops affects rainbow
brightness. Too few sunlit drops
make a faint bow but too many
brighten the background and
swamp the bow.
Forecasting Weather with Rainbows
To see a rainbow look opposite the Sun i. e., to the West in the morning and to the East in
the afternoon. Since storms move from West to East outside the Tropics, the morning
bow heralds an approaching storm and the late afternoon bow indicates a departing storm.
In the tropics storms move from East to West so the late afternoon bow means trouble.
Sun in West,
Bow in East
Sun in East,
Bow in West
Coronas, Glories and Fogbows
are produced when light waves are
diffracted (etc.) as they pass
through and around tiny droplets.
Coronas appear around the Sun or
Moon. Glories appear opposite the
shadow. Fogbows appear opposite
the Sun in a larger arc like
rainbows, but are broader than
rainbows and have little color.
Cloud droplet
A Fogbow at Saguenay
Fjord, Quebec, Canada
Coronas and Iridescence
form around or near the Sun
Paul Neiman: Corona over
Nederland, Colorado
Glories are most often seen when
flying – around the shadow of the
plane. Do Professors fly first class?