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?

The diameter of the objective of a telescope is $3.6 \ m$. The limit of resolution of the telescope for a light of wavelength $540 \ nm$ is

Assertion $(A):$ To increase the resolving power of a telescope,the aperture $(a)$ of the objective lens should be large.
Reason $(R):$ The resolving power of a telescope is given by $\frac{a}{1.22 \lambda}$.

$A$ telescope uses light having a wavelength of $5000 \, \mathring{A}$ and lenses with focal lengths of $2.5 \, \text{cm}$ and $30 \, \text{cm}$. If the diameter of the aperture of the objective is $10 \, \text{cm}$,what are the resolving limit and the magnifying power of the telescope,respectively?

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:

The limit of resolution of an oil immersion objective microscope of numerical aperture $0.8$ for light of wavelength $0.6 \mu m$ is