What is popularly known as 'A smile in the sky' ? How is it produced ?

Explanation

Rainbows are popularly known as 'A smile in the sky'. Nothing seen in the sky has captured the human attention more than a window.
The principles behind the formation of a rainbow are so complex that some are still not fully understood. However we do know that refraction, total internal reflection and dispersion,all play some part in the formation of a rainbow. All we need to produce a rainbow is simultaneous sunshine and rain. Even water drops from a lawn sprinkler can serve the purpose.
Sunlight incident on a water droplet is refracted. Because of dispersion, each colour is refracted at a slightly different angle. At the back surface of the droplet, the refracted rays undergo totqal internal reflection. On the way out of the droplet, light rays are once more refracted and dispersed.
The wavelength seen depend upon the relative positions of sun, droplet and observer. As there are millions of water droplet in the atmoshphere, a complete spectrum is seen. Violet colour is at the inside of teh arc. then blub, green, Yellow and at the outside red. This is the primary rainbow or first order rainbow.
The second order rainbow (or secondary rainbow) occurs when light rays are reflected twice inside the drop before emerging. Newton derived a formula for the angular size of rainbow. The angular size for primary rainbow is `42^(@)` and for secondary rainbow, it is `51^(@)`.