rainbow, high order rainbows, halos, glories

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rainbow, high order rainbows, halos, glories

• CHAN KA YEE
• LEUNG CHUN YI

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PrefaceNot all coloured patches in the sky are
rainbows.

• Rainbows are formed by refraction and reflection
  of sunlight by raindrops.  
• When sunlight passes through ice crystals, halos
  form and they are mostly coloured .    
• Small cloud or fog droplets diffract light to
  form ringed glories.

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Content

• 1. Fundamental laws of optics
• Snells Law of refraction
• Diffraction
• 2. Rainbows
• Primary rainbow
• Secondary rainbow
• Alexanders dark band
• High order rainbow
• Supernumerary rainbow
• Factors affecting rainbow
• 3. Halos
• Different forms of halos
• Ray path in hexagonal ice crystal
• 22degree halo
• Formation
• Reason for 22degree
• 4. Glories
• Backward scattering
• Factor affecting glorys pattern

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Snells Law of refraction

• Where
• VL1 is the longitudinal wave velocity in material
  1.
• VL2 is the longitudinal wave velocity in material
  2

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Diffraction

• Diffraction of light occurs when a light wave
  passes by a corner or through an opening or slit
  that is physically the approximate size of, or
  even smaller than that light's wavelength.

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Rainbows

• refraction and reflection of sunlight by
  raindrops

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Primary rainbows

• One internal reflection
• Its colours are produced by the two refractions
• appearing opposite the sun(anti-solar point)

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Primary rainbowsRaindrop Rays

• Rays further from the centre are deviated less
  and less until the deviation reaches a minimum.
• "Minimum deviation angle " or "rainbow angle".
• The deviation increases once more as the entrance
  ray approaches the drop rim .
• about 137.5º for deep red light

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• Rays cluster strongly around the rainbow angle,
  rays near the rainbow angle form the bow's
  bright outer edge.
• Red light is refracted less than blue and its
  minimum deviation angle is less.
• Red is therefore on the outside of the primary
  bow.
• most intense light at an angle of 4042

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Primary rainbowsRainbow Cone 
 

• rainbows are overlapping bright edged disks
  rather than narrow coloured rings.
• Drops inside the cone brighten the sky inside the
  bow.
• Drops outside the cone send no light into your
  primary bow.
• Each person has their own cone and sees their
  very own rainbow.
• E.g. A rainbow being seen from a car stays fixed
  relative to the sun.

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Primary rainbow colours
 

• The peaks are at angles of minimum deviation.
• Rays deviated more than the minimum deviation
  angle send light inside the bow
• so the light of any particular wavelength falls
  off slowly towards the bow's center.
• All these colours mix to form white inside the
  main bow.

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Secondary Rainbows 
 

• two internal reflections
• rays are deviated more than 180º
• The 51 radius bow occurs at the minimum
  deviation angle of 231.
• colours reversal

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Alexander's Dark Band

• No light from the primary appears more than 42º
  from the center ?brighten the sky inside
• No light from secondary rays appears at less than
  51º ?brighten the sky outside
• ?The sky between is dark.

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High-Order Rainbows

• Each internal reflection weakens the rays ? the
  higher order bows are progressively fainter.
• Look also at how the entrance ray that makes each
  bow grazes closer and closer to the edge of the
  drop? colours spread wider and reduces their
  brightness even further
• Hardly to be seen!

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Supernumerary Rainbows

• Look slightly inside a bright primary bow and
  sometimes you will see one or more predominantly
  green, pink and purple fringes.
• wave nature of light

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Supernumerary Rainbows Formation

• One wave has further to travel through the drop
  than the other.
• When they leave the wave crests are no longer
  always in phase.
• interference? light and dark fringes inside the
  primary bow
• Each bright fringe is a supernumerary bow.
• Each drop size produces differently spaced
  fringes which overlap to a blur. ? Less obvious
  when the rain has drops of widely different
  sizes.

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Factors affecting Rainbowsdrop size

• large drops(several mm in diameter)? narrow bows
  with intense colours
• Smaller drops ? broader bows with less saturated
  colours
• Very small drops ? nearly colourless cloudbows
  and fogbows

• Classically, the intensities of two ray paths
  simply add together
• Classical geometric optics cannot explain!? Wave
  behaviour of light

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• The crests start in step towards the drop
• but, with the different entrance points and path
  lengths ? phase difference and interference
• the drop size decreases ? phase difference
  changes more slowly with the rainbow deflection
  angle
• The main rainbow peak therefore broadens and any
  supernumeraries are more widely spaced.

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drop shape

• Small raindrops are kept strongly spherical by
  surface tension forces.
• Larger drops are sometimes flattened by air
  resistance as they fall and they may even
  oscillate .
• Even small departures from sphericity destroy a
  rainbow.

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Low and High Bows Effect of solar altitude

• At sunrise or sunset, a rainbow's centre, the
  antisolar point, is on the horizon. The rainbow
  is half in the sky, a semicircle.
• As the sun rises, the bow's centre sinks.
  Eventually when the sun is 42º high only the tip
  of the bow is visible above the horizon.

• In the summer, rainbows are best seen in early
  morning or late afternoon when the sun is
  comparatively low.

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• A more complete circle is sometimes visible from
  mountains or aircraft.

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Halos

• A halo is a luminous ring or an arc around the
  Sun or Moon 1
• Common circle of light around the Sun or the Moon
  to a rare event in which it extends across the
  whole
• Round solar halos with a radius of 22 happen
  more often than rainbows .In Europe and parts of
  the United States can be seen on average twice a
  week.

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• Picture from Zen Roxy in Flickr web

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atmospheric halo

• Halo phenomena may take many forms.1
• the common 22 halo
• parhelia (or sundog) luminous spots about 22 on
  either side of the Sun
• A tangent arc associated with the 22 halo
• The large, less luminous halo with an angular
  radius of 46
• the tangent arc to the 46 halo
• the circumzenithal arc, centered on the zenith
  and parallel to the horizon
• The parhelic circle (or sun dog), which passes
  through the Sun and may extend completely across
  the sky

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Q What is the source of halo phenomena?
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Ans Ice crystals in cirrus cloudsAtmospheric
halos are caused by tiny ice crystals in the
atmosphere that refract and reflect incoming
light. Ice crystals in these clouds (at much
lower temperature) are in hexagonal prism
instead of cube
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• SD (from a side to a directly adjacent side)
  can not
• occur in hexagonal type ice crystals because
  of total internal reflection
• LL (a lid to another lid)and SO(from a side
  to an opposite side) paths do not change light
  paths
• The remaining light paths, LS (from a lid to a
  side face), and SF (from a side to a next side
  of a direct neighbor) explain various halo
  phenomena 2

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22 halo

Rays passing through two of their side faces are
deflected through angles from 22? up to a little
bit over 40?, which are expressed as D
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http//www.atoptics.co.uk/halo/circ1.htm
Rotating an ice crystal for formation of 22 ?
halo

• When light rays pass through crystals with all
  possible orientations, there is a concentration
  of rays deviated by angles near 22?
• the direction of the emerging ray changes very
  little as the crystal is rotated several degrees
  from the minimum deviation angle.
• Rays deflected more than 22? produce the outer
  halo light which fades away with increasing
  angular distance from the Sun
• Unlike 22? halos, light rays from top (bottom) to
  side or from side to top (bottom) are responsible
  for 46? halos.

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What is glories

• in the form of concentric colored circles
  surrounding the shadow
• caused by the backscattering of sunlightfrom
  small droplets of water.

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Backward Scattering

 

• The actual path, drawn as a solid line for red
  light, leaves the droplet 14.4º short of the
  demanded 180º.
• To explain the apparently impossible light
  path(dotted line)  
•  We are taking account of another optical
  phenomenon surface waves
• Light travel along the rim as a "surface wave"
  before being refracted.
• Surface waves are strongest for light at grazing
  incidence
• Total internal reflection delays.
• Backward Scattering is possible

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• The glory is still not fully understood, this
  explanation is incomplete - but we are getting
  there

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Factor affecting glorys pattern-droplet size

• glory size is inversely proportional to the
  droplet diameter

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Reference further information

• Atmospheric Optics http//www.atoptics.co.uk/bows
  .htm
• The rainbow (Owen Davies, Jeff Wannell, and John
  Inglesfield, School of Physics and Astronomy
  )http//www.iop.org/activity/branches/South_West/
  Events/file_21809.pdf
• Wikipedia http//en.wikipedia.org/wiki/Rainbows
• Splashing colors everywhere, like a rainbow
  http//www.flyingcircusofphysics.com/pdf/Chapter6_
  Ref_Com.pdf

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• Website
• 1 The Internet Encyclopedia of Science
  http//www.daviddarling.info/encyclopedia/H/halo_a
  tmospheric.htm
• Pictures from wikipedia
• Journal
• 2 A Study on Atmospheric Halo Visualization
• Sung Min Hong and Gladimir Baranoski
• Technical Report CS-2003-26

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Appendix (Rainbows)

• Zero Order Glow 
• If rain is falling between you and the sun there
  will likely be an intense glow.
• It is best seen when the sun is low and already
  orange or red.
• This extra glow, over and above the ordinary sky
  brightness in the sun's direction, is formed by
  light passing through the raindrops and emerging
  the other side without having been internally
  reflected.

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Appendix (halo)

• Factors affect the sharpness of halo?
• 1.When their ice crystals are smaller than
  0.01mm, light is significantly diffracted
• halos are weak and diffuse
• 2.Crystals larger than 0.05mm
• ?refract and reflect light cleanly to produce
  halos
• 3. Crystals have precise alignments and larger
  than 0.1mm
• ?The sharpest halos occur

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Parhelion (Sundog)
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• Plate crystals will tend to fall with the axis
  connecting its flat bases vertical, the flat
  bases oriented nearly horizontally.
• With the sun low in the sky, these plate
  crystals would have the proper orientation to
  refract light to the observer from the sides of
  the halo.
• The better the orientation of the ice crystals,
• the smaller and brighter are the resulting spots
  on either side of the sun 2

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Producing halo in laboratory