A rainbow is a circular arc of concentric colored bands, caused by a combination of refraction and reflection of sunlight by raindrops. (Refraction is the bending of light as it passes from one transparent medium into another transparent medium.) Sunlight striking a shaft of falling raindrops is refracted twice and internally reflected by each drop of rain. A solar ray is refracted as it enters a raindrop. Then, the ray is reflected by the inside back of the drop before being refracted again as it exits the drop. Each person sees his or her own rainbow.
Because of reflection, a rainbow appears to an observer who has his or her back to the Sun and is facing a distant rain shower. A rainbow never forms when the sky is completely cloud covered. The Sun must be shining. For the reason of geometric considerations, the Sun can be no higher than 42 degrees above the local horizon in order for someone on the ground to see a rainbow. If the solar altitude is greater than 42 degrees, then the returning solar rays are not directed towards Earth’s surface. A rainbow is more likely during a morning or evening shower than a shower at noon. At middle latitudes, weather systems usually progress from west to east so that appearance of a rainbow to the east in the early evening usually signals improving weather. Rain showers are moving away toward the east and clearing skies are approaching from the west, where the Sun is setting. A morning rainbow to the west signals approaching rain.
When raindrop refraction disperses sunlight into its component colors, it forms the concentric bands of color of a primary rainbow. From outer to innermost band, the colors are red, orange, yellow, green, blue, and violet. In some occasions, a secondary rainbow appears about 8 degrees above the primary rainbow. Double reflection within raindrops produces the secondary rainbow with the order of colors reversed.
http://www.photocentric.net/rainbow_physics.htm
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