Two vertical poles are at a distance of $6.28 \, m$ from each other. What should be the maximum distance of an observer from the poles to see them separately? (in $km$)

The resolving power of the human eye is $1'$. At what distance $r$ (in $km$) can two objects separated by a distance of $d = 3 \, m$ be seen as distinct?

At Kavalur in India,astronomers using a telescope whose objective had a diameter of $1 \, m$ started using a telescope of diameter $2.54 \, m$. This resulted in:

Wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \; \mathring{A}$ and $\lambda_2 = 5000 \; \mathring{A}$. The ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$) is:

Our eye is most sensitive for which of the following wavelengths in $\mathring{A}$?

Which of the following is the smallest size grain that can be seen using a normal microscope using visible light $(400 \ nm < \lambda < 700 \ nm)$ (in $nm$)?