Explain in brief the formation of a secondary rainbow.

A card sheet divided into squares each of size $1 \mathrm{m}{\mathrm{m}}^2$ is being viewed through a magnifying glass (a converging lens of focal length $10 \mathrm{cm}$) held close to the eye.
(a) At what distance should the lens be held in order to view the squares distinctly with the maximum possible magnifying power?
(b) What is the magnification in this case?
(c) Is the magnification equal to the magnifying power in this case? Explain.

 Why are optical telescopes located in uninhabited places on mountains?

A small telescope has an objective lens of focal length $140 \mathrm{cm}$ and an eyepiece of focal length $5.0 \mathrm{cm}$.
(a) What is the separation between the objective lens and the eyepiece?
(b) If this telescope is used to view a $100 \mathrm{m}$ tall tower $3 \mathrm{k}\mathrm{m}$ away, what is the height of the image of the tower formed by the objective lens?
(c) What is the height of the final image of the tower if it is formed at $25 \mathrm{c}\mathrm{m}$?