Explain the formation of rainbow.

The refractive indices of the material of a lens for violet and red light are $1.56$ and $1.54$ respectively. If the focal length of the lens for violet light is $40 \mathrm{cm}$, then calculate $\left(\mathrm{i}\right)$ focal length for red light and

A flint glas convex lens of focal length $20 \mathrm{cm}$ is placed in contact with a crown glass lens. The refractive indices for blue are red lights of crown and flint glass are respectively $1.523,1.515 and 1.664,1.644$

$\left(\mathrm{i}\right)$ Find the nature and focal length of crown glass lens which will form and achromatic combination with the flint glass lens.