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Why do we see a rainbow in the sky only after rainfall?

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A rainbow is caused by dispersion, refraction and internal reflection of sunlight by tiny water droplets.
We see a rainbow in the sky only after rainfall due to dispersion of sunlight by tiny water droplets, present in the atmosphere due to rainfall. These droplets act as a prism after rainfall, for the rays coming from the Sun. Subsequently, the sunlight after striking the surface of these droplets gets refracted and then gets dispersed into its seven constituent colours. After this, the light rays are subjected to total internal reflection (complete reflection of a ray of light within a medium from the surrounding surfaces back into the medium).
At that point, the rays are again refracted when they come out of the water droplet.
Hence, the rainbow is formed.

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