If a microscope is placed in air,the minimum separation of two objects seen as distinct is $6 \mu m$. If the same is placed in a medium of refractive index $1.5$,then the minimum separation of the two objects to be seen as distinct is: (in $\mu m$)

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 $\,m$)

How to increase the resolving power of a telescope and a microscope?

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:

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:

Two points separated by a distance of $0.1 \, mm$ can just be resolved in a microscope when a light of wavelength $6000 \, Å$ is used. If the light of wavelength $4800 \, Å$ is used, this limit of resolution becomes: (in $mm$)