If the wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \, \mathring A$ and $\lambda_2 = 5000 \, \mathring A$,what will be the ratio of their resolving powers?

In an optical instrument- microscope, the wavelengths of light used are $\lambda_1 = 6800 \text{ Å}$ and $\lambda_2 = 5100 \text{ Å}$. The ratio of the resolving power of the microscope corresponding to $\lambda_1$ to that for $\lambda_2$ is

If an object kept at the least distance of distinct vision is just resolved with light of wavelength $500 \ nm$ and a pupil of diameter $1 \ mm$,at what distance will the object be just resolved if the wavelength is $400 \ nm$ and the pupil diameter is $0.8 \ mm$ (in $cm$)?

Two luminous point sources separated by a certain distance are at $10 \,km$ from an observer. If the aperture of his eye is $2.5 \times 10^{-3} \,m$ and the wavelength of light used is $500 \,nm$, the distance of separation between the point sources just seen to be resolved is (in $\,m$)

The resolving power of a telescope whose lens has a diameter of $1.22 \ m$ for a wavelength of $5000 \ \mathring{A}$ 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 $\frac{a}{1.22 \lambda}$.