In a photometer, two sources of light when placed at 30 cm and 50 cm respectively produce shadows of equal intensities. Their candle powers are in the ratio of

(i) A giant refracting telescope at an observatory has an objective lens of focal length $15 \mathrm{m}$. If an eyepiece of focal length $1.0 \mathrm{c}\mathrm{m}$ is used, what is the angular magnification of the telescope?

(ii) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is $3.48\times {10}^6 \mathrm{m}$, and the radius of lunar orbit is $3.8\times {10}^8 \mathrm{m}$.

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.

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 $25 \mathrm{c}\mathrm{m}$?