The value of numerical aperture of the objective lens of a microscope is $1.25$. If light of wavelength $5000\,\mathring{A}$ is used, the minimum separation between two points, to be seen as distinct, will be....$\mu m$

$A$ telescope is used to observe two objects at a distance of $z = 10 \ km$ which are $s = 0.12 \ m$ apart and illuminated by light of wavelength $\lambda = 600 \ nm$. Estimate the diameter of the objective lens of the telescope if it can just resolve the two objects. Assume diameter $D >> \lambda$ and separation between objects $s << z$. The answer is in $cm$.

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

The resolving power of a microscope depends upon:

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 $\mu m$)

The numerical aperture of a microscope is $0.12$, and the wavelength of light used is $600 \, nm$. Then its limit of resolution will be nearly $............. \, \mu m$.