Title: rainbow, high order rainbows, halos, glories
1rainbow, high order rainbows, halos, glories
- CHAN KA YEE
- LEUNG CHUN YI
2PrefaceNot 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.
3Content
- 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
4Snells Law of refraction
- Where
- VL1 is the longitudinal wave velocity in material
1. - VL2 is the longitudinal wave velocity in material
2
5Diffraction
- 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.
6Rainbows
- refraction and reflection of sunlight by
raindrops
7Primary rainbows
- One internal reflection
- Its colours are produced by the two refractions
- appearing opposite the sun(anti-solar point)
8Primary 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
9- 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
10Primary 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.
11Primary 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.
12Secondary Rainbows
- two internal reflections
- rays are deviated more than 180º
- The 51 radius bow occurs at the minimum
deviation angle of 231. - colours reversal
13Alexander'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.
14High-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!
15Supernumerary 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
16Supernumerary 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.
17Factors 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
18- 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.
19 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.
20Low 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.
21- A more complete circle is sometimes visible from
mountains or aircraft.
22Halos
- 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.
23- Picture from Zen Roxy in Flickr web
24atmospheric 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
25Q What is the source of halo phenomena?
26Ans 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
27- 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
2822 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
29http//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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32What is glories
- in the form of concentric colored circles
surrounding the shadow - caused by the backscattering of sunlightfrom
small droplets of water.
33Backward 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
34- The glory is still not fully understood, this
explanation is incomplete - but we are getting
there
35Factor affecting glorys pattern-droplet size
- glory size is inversely proportional to the
droplet diameter
36Reference 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
37- 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
38Appendix (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.
39Appendix (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
40Parhelion (Sundog)
41- 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
42Producing halo in laboratory