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After the rain a number of small droplets of water remain suspended in the air. Each drop acts as a small prism. When sunlight falls on these drops the white light spills into seven colours. The dispersed light from a large number of drops forms a continuous band of seven colours. 
This coloured band is called a RAINBOW.
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A rainbow is an optical and meteorological phenomenon that is caused by both reflection and refraction of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun
rainbow is an optical and a meteorological phenomenon that is caused by reflection and refraction of light in water droplets resulting in spectrum of light appearing on the sky.rainbows cause by sunlight appear directly opposite to the direction of the sun.rainbows are full circles but they appear like an arc to the viewer because they are illuminated droplets of water on the sky.

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After a rain in the fore noon or after noon when the sun rays are making  angle of 40 to 42 degrees with the horizontal then we have a possibility of  primary rainbow.

See diagram.

First the Sun rays are refracted in to water drops suspended in air some hundreds of meters in to the sky.  Then those light rays are totally internally reflected and then refracted to reach the human eye at a cone angle of 40 to 42 degrees. Red color is visible on top and violet is on the bottom. The dispersion of light takes place at the last refracting surface of water drops.

A secondary rain bow is also formed with violet on top and red below other colors.
It is fainter than the primary rain bow. It is due to two total internal reflections before the light emerges out of the water drops.