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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.


When the white light rays of the sun fall on the rain drops they act as a tiny prism and reflect the light. Then the light splits into the seven colours: red, orange ,yellow ,green ,blue indigo and violet. This is also called the dispersion of light, first defined by Sir Isaac Newton. Hope this helps..... : )
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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. This is visible to us as the VIBGYOR color bands in a semicircular arc in the sky. Actually the rainbow is a full circle within the cones angles of 40 to 42 degrees.

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.