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Rainbows
A sun dog is seen as brightly glowing dots around the sun, because sunlight is refracting off of ice crystals that are plate shaped and seen in the cirrus clouds. You may see them anywhere in the world and you may see them associated with 22 degrees halos. You'll see sun dogs most commonly near sunrise or sunset. They may be reddish in color or bluish in color. Figure 45 shows these interesting sun dog spots:
It is possible to see moon dogs as well. This involves light from the moon and is also refracted off of ice crystals. You often see these when the moon is full or nearly full.
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We have already talked about light pillars, which are seen in Arctic regions as pillars of light emanating from any light source as a light is reflected off of plates of ice crystals. You can also see light pillars associated with the sun or the moon. These are called solar light pillars and lunar light pillars, respectively.
RAINBOWS
Everyone has seen a rainbow. They are beautiful sky phenomena often seen as a multicolored arc after a rainstorm. Light is reflecting off of water droplets after the rain, refracting in ways that spread out the white light into a specific color pattern. The angle of refraction is exactly 42 degrees so you only see the rainbow when you are looking at this angle from the raindrop. Rainbows are combination of reflection and refraction of light.
As sunlight strikes a raindrop, some of it is reflected back off of the raindrop. The rest of it enters the raindrop and gets reflected or bent. Light waves do not get bent at the same angle when they are refracted. The angle of refraction is based on the wavelength of light. This is why refracted light appears as a prism or rainbow of multiple colors.
The radius of any given rainbow depends on the refractive index of the water droplet. Any droplet with a high refractive index or bending ability will produce a small radius of a rainbow. Saltwater has smaller rainbows than freshwater because its refractive index is greater. In reality, rainbows are full circles. You can see these full circles on an airplane but, because of the earth, you only see half of the circle from that vantage point.