Ch. 17 
Everyone is familiar with the appearance of rainbows. But the sky can exhibit a wide variety wonderful (as well as beautiful) patters due to the optics of water drops and ice crystals. Here we will look at just a few examples. Most of the pictures you will see in this lecture are from a gorgeous book co-written by a friend of mine: Color and Light in Nature (by David K. Lynch and William Livingston, Cambridge University Press), now in its second edition. It is simply the most beautiful book covering this and other related subjects. Another fun book to read is Craig Bohren’s Clouds in a Glass of Beer: Simple Experiments in Atmospheric Physics. Both are available in paperback.
The Earth’s Shadow
One of the most common, but
overlooked, phenomena is something that is best seen on a clear cloudless day the shadow of the Earth! If you look at
the sky near the horizon just after sunset, or just before sunrise, the shadow
of the Earth is projected onto the sky.
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Just above the dark band is a zone of the sky brighter than the rest. This is the anti-twilight arch. It is a little brighter than the rest of the air still catching the rays of sunlight because of the way light scatters off of air molecules and other particles in the atmosphere. Much of the light is scattered in the forward (nearly original) direction, but there is often a relatively strong “backscattered” component that is the source of the ATA. |
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Of course, if the whole Earth can cast a shadow, so can parts of it. One regular activity that my colleagues and I do when observing from the mountaintop on the Big Island in Hawaii is to watch the shadow of the mountain near sunrise and sunset. Here are three pictures I took in 2003.
Dave Lynch and the morning shadow of Mauna Kea at sunrise.
The shadow of Mauna Kea at sunset.
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If you view the mountain shadow from the side, sometimes you can see a “mountain spike” that runs from the top of the mountain to the top of the shadow of the mountain. |
Clouds
Rainbows
The rainbow is the best-known of these optical phenomena.
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The combination of light refracting at the surface of a spherical droplet of rain (real raindrops do not have a teardrop shape!), followed by an internal reflection and a second refraction as the light exits the drop naturally concentrates the light at an angle of 42° from the antisolar direction. Because refraction is involved, this light will undergo dispersion so that each color follows a slightly different path. The result is a series of concentric colored bands. If the sun is close to the horizon, you can see almost half of the bow. If the sun is 42° or more above the horizon, you will not see any rainbow. Also note that for the primary rainbow, blue is on the “inside” and red is on the “outside”. You would be amazed at how often the colors are reversed in paintings from previous centuries!
If the light hits close to the edge of the drop, the angles are right for two internal reflections, and a secondary bow can be seen! And for the secondary bow, the order of the colors is reversed from that of the primary bow.
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In the region between the primary and secondary bows is a dark band where no (or essentially no) light gets back to the observer. This is Alexander’s Dark Band (named for Alexander of Aphrodisias who described it ca. 200 AD).
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Sometimes if you look very carefully at a really bright rainbow, you can see multiple thin colored bands within one of the bows, These are supernumary bows. It is currently thought that these are due to interference effects.
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A nice demonstration of how the properties of the rainbow are related to the index of refraction of water can be seen by looking at one over the ocean, while ocean spray is being lofted in the same area.
Here you can see that the diameter of the circular band that makes up the bow is smaller for salt water droplets, because the index of refraction for salt water is higher than it is for fresh water. |
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Fogbows
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Sometimes a thin haze of fog will exhibit a bow. The picture of this fogbow was made overlooking a valley adjacent to Mauna Kea.
One evening while returning up the mountain, we saw a fogbow due to the Moon! We could see it on the roadway only a few feet from our shoes. Unfortunately, no picture…….. |
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Glories, Coronae, Heligenschein, etc.
Often the conditions are
right to see a round patch of colored light immediately around the Sun or Moon.
This is called a corona (“crown”). It is white in the center, and then colored
successively with blue, green, yellow, and red rings. It is produced by the
diffraction of light around the water droplets. Remember Rayleigh’s criterion
from the lecture on instruments. Same thing, except now it is a round obstacle
instead of a round hole! (As it turns out, these produce mathematically
identical results a phenomenon called Babinet’s
Principle).
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Sometimes, deep rich (almost “metallic”) colors can be seen in corona-like regions further from the Sun. These “mother-of-pearl” colors are called iridescence or irisation.
Once, when I was visiting Boulder, Colorado, I saw a spectacular band of clouds exhibiting irisation that stretched for miles at the top of the Rocky Mountains. |
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Once seen only rarely, the glory is now a common sight seen from airplanes. Before the advent of air travel, people would see this bright ring surrounding the shadow of their head cast onto nearby clouds. It was as if they were wearing their own personal halo!
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Three phenomena in one! Here you can see a fogbow, a glory, and the Spectre of the Brocken.
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A related phenomenon is heligenschein, where you see backscattered sunlight from water droplets suspended just above leaves by tiny hairs.
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Summary of Phenomena
Blue Moons & Suns
Regardless of what anyone tells you to the contrary, the blue moon is a real observable phenomenon, although quite rare. You can also see a blue sun. All you need is the right sized particles in the atmosphere. If their sizes are close to the wavelength of light, this phenomenon can result. This can occur if a major volcanic eruption has lofted a lot of dust into the atmosphere. But water droplets can do the same thing.
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Left Right - the scattering efficiency of droplets versus wavelength. The sizes of the droplets are labeled. Note that a 600 nm droplet scatters red light out of the beam, allowing the blue light past unaffected. In this case, a blue Sun or Moon can result. |
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Ice Crystals
In my own personal opinion, the most interesting phenomena occur due to the effects that ice crystals produce. These may be due to thin high-altitude clouds, or blowing snow. Most people have seen a halo around the Moon at night or the Sun in the daytime. These are due to dispersion as tiny ice crystals in the atmosphere act like little prisms.
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Think of the crystals as hexagonal plates or rods. Depending on whether the light strikes one of the 6 rectangular faces on the “sides” or on of the 2 hexagonal faces on the “ends”. The light will be deviated by ~22° or ~44°, and it will, of course be different for different wavelengths due to dispersion. For halos, the red is on the inside and blue on the outside. But because it makes a difference what the crystal’s orientation is (unlike a spherical water drop) the crystals must be largely aligned. Flat plate crystals can float downward like falling leaves, thus providing the alignment. Bigger crystals can tumble,
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Often, one sees a parhelic circle, running around the sky at the same altitude as the Sun above the horizon. Where this crosses the 22° halo, one gets an extreme brightening if the crystals are well-aligned. These are parhelia, or more commonly referred to as sundogs. They are often highly colored. A few years ago I saw one while on campus that was so bright it was almost difficult to look at! |
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There are also solar pillars, circumzenithal arcs, circumscribed halos, Parry arcs, etc., etc.
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Solar pillar |
Artificial pillars |
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