Atmospheric Optics - Institute for Astronomy

Atmospheric Optics

Karen J. Meech, Astronomer

Institute for Astronomy

Lecturer: Jan Kleyna

Electromagnetic Radiation

!  Characterized by !, f, c !  Speed c = 3x105 km/s in vacuum !  Velocity not constant in other media

!  Because of charge separation " slowing

!  Index of refraction: n = c/v !  Speed decreases for shorter !, hard to

get molecule to oscillate !  Results in dispersion

Medium n Air 1.0003

Water 1.333 Glass 1.4-1.9

Medium n CO2 1.00045

Benzene 1.501 Diamond 2.419

Huygen’s Principle (1678) !  Wave theory for light !  Model for behavior !  Not a physical theory !  Light as a wavefront

!  Think of an advancing ‘plane wave’ as a set of point-like emitters (1)

!  The spherical waves from the points add up and cancel out to make a new plane wave a moment later (2)

!  ... so wave advances

(1) (2)

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Wave Nature Implies Refraction (bending)

Air (fast, n≅1)Glass (slow, n>1.4)

!  Mechanism !  As waves travel from faster

medium (air) to slower (glass) the wave front slows

!  If light hits the boundary at an agle, one side of front slows first

!  The light bends !  Analogy

!  Tires on one side of wagon slow down in mud, and wagon turns toward the mud

At each interface there is both

!  Light bent towards the perpendicular nlow " nhigh

!  Light bent away from perpendicular nhigh " nlow

"1#

"2#

n1

n2 > n1

n2 < n1 "2#

Refraction Reflection

!  ! = Angle of reflection = Angle of incidence

Dispersion

1 2

•  How does a prism work? •  nair = 1.0003 < nglass ~ 1.5 •  1 - bent toward ⟂ •  2 - bent away from ⟂

• Recall that nglass changes with wavelength

• blue refracts more than red • higher frequency " bent

more " dispersion of white light into spectrum

Applications: Atmospheric Refraction

!  Starlight passes from vacuum, n=1.000 into the atmosphere, n=1.0003

!  Density of air increases at lower altitudes " n changes !  As n increases, light is bent continuously, deflecting star !  Blue light bent the most

!  “Differential refraction” " colorful stars, especially near horizon

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Green Flash – Atmospheric Refraction

!  Differential refraction !  Uppermost part of sun’s disk

is bluer when near horizon

!  Sun sets !  Red sets first !  Green / Blue sets last because air is bending it over horizon

!  Blue hard to see because of atmospheric scattering !  Sky is blue, which means that atmosphere scatters blue light in all

directions instead of transmitting it !  Thus green is usually the last visible bit of the sun

Green flash really has several types, involving multiple refraction phenomena, including mirages - for more information, see

http://mintaka.sdsu.edu/GF/papers/Zenit/GF.html

Demo Break

! Refraction at different angles ! Scattering vs. Absorption in Atmosphere ! Greenflash !  Interstellar reddening & extinction !  “Seeing”

The Rainbow !  Rene Descartes 1637

!  rainbow physics from experiments with glass spheres filled water

!  Rainbow is seen !  42o away from anti-solar

direction

!  Each person has a “personal” rainbow

!  you see blue at angles where the droplets send just blue light into your eye

From Sun

Rainbow Formation

!  Combination of refraction & reflection at each interface !  Light entering perpendicular – passes

through w/o refraction !  Light enters at angle refracted &

reflected at each boundary " light loss !  Dispersion of different ! of light occurs

!  Light at back of drop: refracted & reflected !  Light returns to front of drop

!  Light farther from central axis " refracted farther until reaching a critical point !  At critical point, rays cross

!  Raindrop: water !  n = 1.333

!  In Air !  n = 1.0003

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Tracing rays of light in a sphere of water !  Rays from 2"7 emerge

farther from center !  Beyond ray 7, refracted ray

moves toward center !  Light bunches up (gets

brighter at crossover) !  Angle between ray 1 and 7 is

~42o " this is the RAINBOW

!  Red refracted least " on outside of rainbow

A rainbow arises from the special geometry of reflection+ refraction in a sphere, plus dispersion

IN

OUT

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Circular Rainbows

!  Only visible from certain geometric perspectives " above the ground

!  Only visible from certain geometric perspectives " above the ground

You are at the ocean. You see a rainbow in the salt spray. You know that salt water has a slightly larger index of refraciton than fresh water. The salt spray rainbow has an angular diameter that is:

A.  Smaller than normal (freshwater) rainbow B.  Larger than a normal rainbow

C.  The same size as a normal rainbow D.  It depends on the angle of the sun

?°Clicker: Discuss in Groups

You are at the ocean. You see a rainbow in the salt spray. You know that salt water has a slightly larger index of refraciton than fresh water. The salt spray rainbow has an angular diameter that is:

A.  Smaller than normal (freshwater) rainbow B.  Larger than a normal rainbow

C.  The same size as a normal rainbow D.  It depends on the angle of the sun

?°Clicker: Second chance

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Answer: A - smaller, because index of refraction is larger, so light is refracted more, so rainbow angle is less than 42°

41.2°

photo Dijkema & Konnen; http://www.atoptics.co.uk/rainbows/seabow.htm

Secondary Rainbows !  At the interface where the primary bow rays emerge, there is also an internal reflection !  At the next interface this

wave is reflected and refracted.

!  The refracted ray emerges, bunches up at 51o " the secondary bow

!  Colors are reversed !  because of an added

reflection !  Blue on outside, red inside

!  3rd and 4th rainbows !  on opposite side of drop

(away from observer & not seen)

!  5th rainbow !  is too faint to see outside of

a lab

NSTA Science Objects: http://home.southernct.edu/~gravess1/projects/nsta_object/4_rainbows_b.html

Rainbow Features

!  Primary: Red on outside !  Red is refracted least

!  Secondary: Red on inside !  Internal reflection

!  Brighter region inside first bow !  all light that hits droplets is

scattered inside 42° critical angle, so region inside rainbow is bright

Bright Region

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What happens to rainbow if droplets are not spheres?

A. Droplets have to be very close to spherical. If they aren’t, there’s no rainbow.

B.  If droplets aren’t spheres, the rainbow won’t be circular, but will be flattened or elongated.

C. If droplets are circular along some direction (or axis), then some parts of the rainbow will form, leading to a 42° circular (but broken or incomplete) rainbow.

D. Flat droplets lead to a rainbow larger than 42°, and elongated droplets to a rainbow smaller than 42°.

23 Hint - think of a water glass

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Answer: C

The dimension of a droplet that is circular will lead to a rainbow. The non-circular dimensions won’t lead to a rainbow. So non-circular droplets lead to broken rainbows that still obey the 42° rule.

Raindrop Shape Effects

!  Rainbows require a circular cross section

!  Raindrops can be large !  gravity distorts shape

!  Rainbow seen only at certain orientations !  Corresponds to horizontal circular

cross section

Fogbows & Redbows !  Fogbow

!  Very tiny droplets suspended in cloud/mist

!  Same physics, colors overlap !  Bow looks white because

wavelength becomes larger compared to drop size - geometrical optics doesn’t quite work and colors blend

!  Red Rainbow !  Blue light is more easily

scattered in atmosphere !  Remaining light mostly red,

orange, yellow

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What is Wrong with this Picture?

A. Colors not reversed on 2nd rainbow

B. 3rd bow should not exist

C. Hillside not illuminated

D. Region inside first bow is not bright

E. A,B, C, and D

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Answer: E (all of the above)

What other things are wrong with it?

A. Colors not reversed on 2nd rainbow

B. 3rd bow should not exist

C. Hillside not illuminated

D. Region inside first bow is not bright

E. A,B, C, and D

Alien Rainbows?

!  n = 1.333 !  n = 0.749

Atmospheric Structure !  Troposphere cools with

increasing altitude !  T < 273K until ionosphere !  Clouds contain ice crystals

!  Water ice has hexagonal structure

Ice Crystals in the Atmosphere

!  Ice crystals refract and reflect light !  (n = 1.309)

!  Displays affected by: !  Different crystal shapes !  Different light paths

through crystals

!  Give information on ice in the upper atmosphere

Ice Crystal Refraction - Halos

!  Flat (plate) hexagonal crystals: prisms !  Rays deflected through many angles

(22 to 50 deg) depending in incidence angle

!  Colors !  Red refracted least " inside !  Blue refracted most " outside

!  Orientation !  Minimum angle of deviation 22o

!  Random " 22o halo !  Parallel to Earth " horizontal parts

only " “Sundog”

" = 22o

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Halos: Why do randomly oriented crystals cause a ring?

Many different rotation angles cause a deflection very close to 22°.

Halos & Sundogs (Parhelia)

!  Sundogs – most often seen when sun is low

Sun Pillars

!  Reflection of light from flat plate crystals !  Intensity & height depends on crystal

orientation !  Pillars can be any color

Sunset Pillar Moon Pillar Venus Pillar

Complex Displays •  CZA

•  horiz. ice crystals; light enters through top face and exits side face

•  UTA •  Long, horizontal oriented

cyrstals •  Like 22o halo or sundog •  Except for crystal orientation

•  Parhelic circle •  Reflection of light from vertical

ice crystals •  Simple, or internal with color

dispersion •  LTA

•  Long, horizontal crystals, the twin of the UTA

Tangent Arcs & Circumscribed Halos

!  Formed by pencil shaped crystals !  Shape of arc depends on sun’s elevation !  Special crystal orientations occur for a narrow

range of sizes: 0.05 – 2 mm; otherwise random

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22° halos exist because

A.  Hexagonal ice crystals align in the sky to focus sunlight at the observer like a lens

B.  Hexagonal ice crystals populate the sky at all possible random orientations, but lots of these random orientations refract incoming light at close to 22°

C.  Hexagonal ice crystals block light coming directly from the sun, but reflect light from the sides at 22°

D.  A 22° halo is the third rainbow, between the sun and the observer

E.  None of the above

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Answer: B

Hexagonal ice crystals populate the sky at all possible random orientations, but lots of these random orientations refract incoming light at close to 22°

If you rotate a hexagonal ice crystal while shining light through it, the outgoing light will be refracted at 22° for a disproportionately large part of the rotation. So if you observe at a random cloud of hexagonal ice crystals, a disproportionate number will be refracting incoming light at 22°. picture here

Parry Arcs (rare:first seen during 1820 arctic expedition)

!  Appearance similar to tangent arcs !  crystal horizontal and top/bottom

faces are horizontal !  how this happens still under study

(2010) !  Clusters of pencil crystals? !  Distorted/flattened crystals?

Altitude of Sun

Complex Parry Display

Lowitz Arcs

!  More rare than Parry arcs !  Horizontally aligned plate crystals spin

horizontally? !  Origin now in question. !  3 ray paths give 3 different arcs (upper, lower,

middle)

Middle

Upper

Lower

Lowitz Arc Display

More Complex Displays

Atmospheric Archaeology

!  Computer simulations can untangle the optics

!  This gives knowledge about ice crystals in Earth’s atmosphere 100’s of years past!

!  There are many records of atmospheric light displays

Hevelius “Seven Suns” 1662

!  Gdansk – 2/20/1661 !  Sun 26o above horizon !  22o halo, 46o halo !  22o parhelia (sundogs) !  Upper tangent arc

!  Simulation !  Pencil crystals, long axes horizontal !  Reflection from end faces of pencils !  Plate crystals for sun dogs

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Review

!  Rainbows are caused by !  refraction, reflection, and dispersion

inside water droplets.

!  Complex displays !  Sunlight reflecting and refracting in

hexagonal crystals of ice high up in atmosphere can cause complex patterns in the sky, depending on !  light path in crystal !  alignment of crystals in the sky

Randomly oriented ice crystals (halo)

Flat hexagonal plates

Horizontally aligned ice crystals

Parry aligned ice crystals (horizontal and flat face on top)

All of them together recreate Parry Arctic Expedition display of 1820

Demo Break

!  Halo Sim Software !  free - runs on Windows (or

Mac with PlayOnMac)

! www.atoptics.co.uk

!  St. Petersburg Display of 1790

Compare computation to Lowitz drawing from 1790

Doesn’t look exactly identical: different sky-map projections, like different camera lenses

Supernumerary Bows

!  Like the 42° droplet path, but cannot be explained by Geometric optics

!  Interference between optical paths close together in water drops (like an oil slick)

!  Seen only when drops are very small and of same size - a first proof (1803) that light was made of waves

[*] image from http://www.itp.uni-hannover.de/~zawischa/ITP/refraction.html

*

Optical Effects in Mists !  Water in clouds, mists, fog

!  10-1000x smaller than raindrops !  Wave properties of light

important !  Diffraction Features

!  Corona – rings around the sun !  Glory – ringed phenomena opposite

the sun !  Spectre de Brocken !  Iridescent Clouds !  Heligenschein

Interference – Light superposition

!  Light is a wave !  Amplitude of wave related

to intensity (or brightness)

!  Combining EM radiation !  add amplitude of wave !  In phase: n!, double !  Out of phase n!/2 " 0

Diffraction !  Passing light through a slit !  Use Huygen’s model !  Each point along slit " new waves !  If pathlength in phase " constructive:

a sin " = n!#!  Pathlength out of phase " destructive:

a sin " = n!/2 !  Rules of thumb

!  " is larger for large ! " red outside !  " is larger for small a " big rings =

small drops !  Any obstacle works " water drops

in cloud

Demo – single slit diffraction

Coronae !  Visible as a ring of colors around the sun or moon

!  Ring is close to light source (few degrees) a sin" = n !/2

first dark ring, n = 1; solve for a a = !/2 / sin" 6500/2 / sin (5) = 3.7x104 A a = 3.7 microns

!  Particles must be small! !  Any substance ok: water, ice,

dust, pollen

!  Multiple sizes " white ring !  More commonly seen around

Moon than sun (brightness)

o

Lunar Corona

!  Corona around moon (A. Rahm, 5/26/02) !  Simulation: 3 µm drops

Effect of Particle Sizes

!  Multiple sizes " colored rings overlap " white !  Particles get large " less diffraction, smaller

rings

Glory, Specter de Brocken !  Glory

!  Diffraction effect – anti-solar direction (still debated)

!  Specter de Brocken !  Seen on Brocken

mountain in Germany !  Glory + 2D or 3D shadow

Cloud Irridescence

!  Diffraction effect !  maps out changing cloud

particle sizes

!  Nacreous clouds !  Polar stratospheric clouds 25

km high !  High winds !  10 µm ice crystals !  Often brighter, long lasting

Heiligenschein

!  Dew drops on tips of grass !  Large drops " Geometric

optics, not diffraction !  Focus sunlight !  Light scattered back through

drop in direction of sunlight !  A bit like a bicycle reflector

The Opposition Effect

!  Opposition Effect !  Enhanced backscattering !  Shadow covering !  Any particulate surface

Other Gases?

!  Carbon Dioxide ice !  cubic, octahedral, and cubo-octahedral

Alien Displays – Mars !  Mars Atmosphere

!  95% CO2

!  P = 0.006 bar !  Index of refraction

gaseous CO2: 1.00045

!  Simulation !  22o halo – water ice !  Cuboctahedral CO2 ice "

26o halo !  Cuboctahedral plates –

tangent arcs & parhelia

CO2 – different ice crystal structure

Mars CO2 Atm Ice Simulation

Jupiter !  NH3-rich atmospheres !  Highest clouds, -110oC !  Ammonia forms crystals with cubic symmetry !  Slightly greater index of refraction than for CO2

!  Unknown ice properties at greater depths " cannot predict optics

!  NH3-rich atmosphere; !  Crystals form at greater depths in atmosphere

Alien Worlds – Saturn

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Match the following phenomena to their physical basis (every physical basis may not be

be listed for each phenomenon)

1) Rainbows 2) Supernumerary rainbows 3) Sundogs 4) Opposition brightening

A. 1) reflection 2) refraction 3) refraction and reflection 4) diffraction

B. 1) diffraction 2) refraction 3) refraction 4) shadow enhancement

C. 1) refraction and internal reflection 2) refraction, internal reflection, and diffraction 3) refraction 4) shadow hiding

D. 1) refraction and internal reflection 2) refraction 3) diffraction 4) shadow hiding

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Answer: C 1.  In rainbows, internal reflection deflects light at 42°, and

refraction (including dispersion) spreads it into a spectrum

2. Supernumerary rainbows are rainbows, with diffraction by small equally sized water droplets - classical geometric optics doesn’t explain them (but light path in droplets is still like normal rainbows)

3. Sundogs are created by refraction of light through vertically oriented hexagonal ice crystals

4. Opposition brightening occurs when an observer is between a surface and the sun, so surface is seen from the top, and the shadows caused by bumps in the surface are hidden 77