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Home , Atmospheric refraction, Green flash, Horizon, Sky

Electromagnetic Atmospheric Radiation

! Characterized by !, f, c ! Speed c = 3x105 km/s in vacuum ! Velocity not constant in other media ! Because of charge separation " Karen J. Meech, slowing Astronomer ! Index of : n = c/v ! Speed decreases for shorter !, hard to Institute for get molecule to oscillate ! Results in Medium n Medium n

Air 1.0003 CO2 1.00045 Water 1.333 Benzene 1.501 Glass 1.4-1.9 Diamond 2.419

Wave Nature Implies Refraction Huygen s Principle (1678) ’ (bending) ! Wave theory for ! Mechanism ! Model for behavior Air (fast, n≅1) ! As waves travel from faster (1) (2) ! Not a physical theory Glass (slow, n>1.4) medium (air) to slower (glass) ! Light as a wavefront the wave front slows ! If light hits the boundary at an ! Think of an advancing ‘plane wave’ as a set of point-like emitters (1) agle, one side of front slows first ! The spherical waves from the points add up and cancel out to make a ! The light bends new plane wave a moment later (2) ! Analogy ! ... so wave advances ! Tires on one side of wagon slow down in mud, and wagon turns toward the mud 4

At each interface there is both Dispersion

Refraction Reflection • How does a work?

• nair = 1.0003 < nglass ~ 1.5 1 • 1 - bent toward ⟂ 2 " n1 1# • 2 - bent away from ⟂ " 2# n < n 2 1 • Recall that nglass changes n2 > n1 "2# with wavelength • blue refracts more than red ! Light bent towards the ! ! = of reflection • higher frequency " bent perpendicular nlow " nhigh = Angle of incidence more " dispersion of white light into spectrum ! Light bent away from

perpendicular nhigh " nlow Applications: – Atmospheric Refraction

! passes from vacuum, n=1.000 into the ! Differential refraction , n=1.0003 ! Uppermost part of ’s disk ! increases at lower altitudes " n changes is bluer when near ! As n increases, light is bent continuously, deflecting ! Sun sets ! Blue light bent the most ! Red sets first ! “Differential refraction” " colorful , especially near horizon ! Green / Blue sets last because air is bending it over horizon ! Blue hard to see because of atmospheric scattering ! 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 - for more information,8 see http://mintaka.sdsu.edu/GF/papers/Zenit/GF.html

! Rene Descartes 1637 Demo Break The ! rainbow physics from experiments with glass ! Refraction at different From Sun spheres filled water ! Scattering vs. Absorption in Atmosphere ! Rainbow is seen ! Greenflash ! 42o away from anti-solar direction ! Interstellar reddening & ! “Seeing” ! Each person has a “personal” rainbow

! you see blue at angles where the droplets send just blue light into your Rainbow Formation Tracing rays of light in a sphere of water

! Rays from 2"7 emerge farther from center ! Combination of refraction & reflection at each interface ! Beyond ray 7, refracted ray IN moves toward center ! Light entering perpendicular – passes through w/o refraction ! Light bunches up (gets ! Light enters at angle refracted & brighter at crossover) reflected at each boundary " light loss ! Angle between ray 1 and 7 is ! Dispersion of different ! of light occurs ~42o " this is the RAINBOW ! Light at back of drop: refracted & OUT reflected ! Red refracted least " on ! Light returns to front of drop outside of rainbow ! Light farther from central axis " ! Raindrop: water A rainbow arises from the special refracted farther until reaching a critical ! n = 1.333 point geometry of reflection+ refraction ! In Air ! At critical point, rays cross in a sphere, plus dispersion ! n = 1.0003 14

Circular Answer: A - smaller, because index of refraction is larger, so light is refracted

! Only visible from more, so rainbow angle is less than 42° ! Onlycertain visible geometric from certain geometric perspectives " 41.2° perspectivesabove the ground " above the ground

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

! At the interface where the Secondary Rainbows primary bow rays emerge, Rainbow Features there is also an internal reflection ! At the next interface this ! Primary: Red on outside wave is reflected and refracted. ! Red is refracted least ! The refracted ray emerges, ! Secondary: Red on inside bunches up at 51o " the secondary bow ! Internal reflection ! Colors are reversed ! Brighter region inside first bow ! because of an added ! all light that hits droplets is reflection scattered inside 42° critical angle, ! Blue on outside, red inside so region inside rainbow is bright ! 3rd and 4th rainbows ! on opposite side of drop (away from observer & not seen) Bright Region NSTA Science Objects: ! 5th rainbow http://home.southernct.edu/~gravess1/projects/ ! is too faint to see outside of nsta_object/4_rainbows_b.html a lab Raindrop Shape Fogbows & Redbows

Effects ! Fogbow ! Very tiny droplets suspended in /mist ! Same physics, colors overlap ! Rainbows require a circular cross section ! Bow looks white because wavelength becomes larger ! Raindrops can be large compared to drop size - ! gravity distorts shape geometrical optics doesn’t quite ! Rainbow seen only at certain work and colors blend orientations ! Red Rainbow ! Corresponds to horizontal circular ! Blue light is more easily cross section scattered in atmosphere ! Remaining light mostly red, orange, yellow

Alien Rainbows? Atmospheric Structure

! Troposphere cools with ! n = 1.333 ! n = 0.749 increasing altitude ! T < 273K until ionosphere ! Clouds contain ice crystals ! Water ice has hexagonal structure

Ice Crystal Refraction - Halos Ice Crystals in the Atmosphere

! Ice crystals refract and ! Flat (plate) hexagonal crystals: reflect light " = 22o ! Rays deflected through many angles ! (n = 1.309) (22 to 50 deg) depending in incidence angle ! Displays affected by: ! Colors ! Different crystal shapes ! Red refracted least " inside ! Different light paths ! Blue refracted most " outside through crystals ! Orientation ! Give information on ice ! Minimum angle of deviation 22o in the upper atmosphere ! Random " 22o halo ! Parallel to " horizontal parts only " “Sundog” Halos: Why do randomly oriented Halos & Sundogs (Parhelia) crystals cause a ring?

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

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! Sundogs – most often seen when sun is low ! Reflection of light from flat plate crystals ! Intensity & height depends on crystal orientation ! Pillars can be any color

Sun Pillars

Sunset Pillar Pillar Pillar • CZA • horiz. ice crystals; light enters Complex Displays through top face and exits side face • UTA • Long, horizontal oriented cyrstals • Like 22o halo or sundog • Except for crystal orientation • Parhelic • Reflection of light from vertical ice crystals • Simple, or internal with color dispersion • LTA • Long, horizontal crystals, the twin of the UTA Tangent Arcs & Parry Arcs Circumscribed Halos (rare:first seen during 1820 arctic expedition)

Altitude of Sun

! Appearance similar to tangent arcs ! crystal horizontal and top/bottom ! Formed by pencil shaped crystals faces are horizontal ! Shape of arc depends on sun’s elevation ! how this happens still under study (2010) ! Special crystal orientations occur for a narrow ! Clusters of pencil crystals? range of sizes: 0.05 – 2 mm; otherwise random ! Distorted/flattened crystals?

Complex Parry Display Lowitz Arcs

Middle ! More rare than Parry arcs ! Horizontally aligned plate crystals spin horizontally? ! Origin now in question. Upper ! 3 ray paths give 3 different arcs (upper, lower, middle)

Lower

Lowitz Arc Display More Complex Displays Atmospheric Archaeology Hevelius “Seven ” 1662 ! There are many records of atmospheric light displays ! Gdansk – 2/20/1661 ! Sun 26o above horizon ! 22o halo, 46o halo ! 22o parhelia (sundogs) ! Upper tangent arc ! Computer simulations can ! Simulation untangle the optics ! Pencil crystals, long axes horizontal ! Reflection from end faces of pencils ! This gives knowledge about ice ! Plate crystals for sun dogs crystals in Earth’s atmosphere 100’s of years past!

Review Randomly oriented ice crystals (halo)

! Rainbows are caused by ! refraction, reflection, and dispersion inside water droplets. ! Complex displays ! 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

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Flat hexagonal plates Horizontally aligned ice crystals All of them together recreate Parry Arctic Parry aligned ice crystals Expedition display of 1820 (horizontal and flat face on top)

Compare computation to Demo Break Lowitz drawing from 1790

Doesn’t look exactly identical: ! Halo Sim Software different sky-map projections, like ! free - runs on Windows (or different camera lenses Mac with PlayOnMac) ! www.atoptics.co.uk

! St. Petersburg Display of 1790

Supernumerary Bows * Optical Effects in Mists

! Water in , mists, ! 10-1000x smaller than raindrops ! Wave properties of light important ! Diffraction Features ! Corona – rings around the sun ! Glory – ringed phenomena opposite ! Like the 42° droplet path, but cannot be explained by the sun Geometric optics ! Spectre de Brocken ! Interference between optical paths close together in water ! Iridescent Clouds drops (like an oil slick) ! Heligenschein ! 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 ! Passing light through a slit Diffraction Interference – Light superposition ! Use Huygen’s model ! Each point along slit " new waves ! If pathlength in phase " constructive: ! Light is a wave a sin " = n!# ! Pathlength out of phase " destructive: ! Amplitude of wave related a sin " = n!/2 to intensity (or brightness) ! Rules of thumb ! " is larger for large ! " red outside ! Combining EM radiation ! " is larger for small a " big rings = small drops ! add amplitude of wave ! Any obstacle works " water drops ! In phase: n!, double in cloud ! Out of phase n!/2 " 0

Demo – single slit diffraction

Coronae ! Visible as a ring of colors Lunar Corona 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" o 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 ! Corona around moon (A. Rahm, 5/26/02) ! More commonly seen around ! Simulation: 3 µm drops Moon than sun (brightness)

Effect of Particle Sizes 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

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

! Opposition Effect ! Dew drops on tips of grass ! Enhanced backscattering ! Large drops " Geometric optics, not diffraction ! Shadow covering ! Any particulate surface ! Focus sunlight ! Light scattered back through drop in direction of sunlight ! A bit like a bicycle reflector

Other Gases? Alien Displays –

! Mars Atmosphere ! Simulation ! o ! 95% CO2 22 halo – water ice ! P = 0.006 ! Cuboctahedral CO2 ice " 26o halo ! Index of refraction ! gaseous CO2: Cuboctahedral plates – 1.00045 tangent arcs & parhelia

! Carbon Dioxide ice ! cubic, octahedral, and CO2 – different ice crystal cubo-octahedral structure Mars CO2 Atm Ice Simulation

! NH3-rich ! 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

Alien Worlds – Saturn

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