Please explain how total internal reflection of incident sunlight in a tiny water droplet helps different colours of a rainbow reach the observer's eye.

Dear Student,
Rainbow is a natural spectrum of sunlight in the form of bow which we can see in the sky when the sun shines on rain drops. It is a combined result of reflection, refraction and dispersion of sunlight from water droplets in atmosphere.
When a sunlight enters into a spherical raindrop, it gets refracted and dispersed. The different colours bent in different angles. When different colours of light falls on the back inner surface of drop, water drop reflects different colours of light internally. This is called total internal reflection. The water drops again refracts the different colours when it comes out from the raindrop. After leaving the drop, different colours from the raindrop reach our eye. This is how rainbow is formed.



An important point to be noted here is that a rainbow is always formed in a direction opposite to that of the Sun.
Regards

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