In telescopes, for a given wavelength, the objectives with large aperture are used for

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:

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 diameter of the objective of the telescope is $0.1 \ m$ and the wavelength of light is $6000 \ \mathring{A}$. Its resolving power would be approximately:

Assuming the human pupil to have a radius of $0.25 \ cm$ and a comfortable viewing distance of $25 \ cm$,the minimum separation between two objects that the human eye can resolve at $500 \ nm$ wavelength is nearly: (in $\mu m$)

Two points separated by $0.05 \, mm$ can just be inspected in a microscope when light of wavelength $6000 \, \mathring{A}$ is used. If light of wavelength $3000 \, \mathring{A}$ is used,then the limit of resolution becomes ........... $mm$.