$A$ microscope has an objective of aperture $8 \text{ mm}$ and focal length of $5 \text{ cm}$. The minimum separation between two objects to be just resolved by the microscope is (wavelength of light used $= 5500 \text{ Å}$) (in $\mu\text{m}$)

The resolving limit of a healthy human eye is about:

$A$ microscope was initially placed in air (refractive index $1$). It is then immersed in oil (refractive index $2$). For a light whose wavelength in air is $\lambda$,calculate the change of the microscope's resolving power due to oil and choose the correct option.

Resolving power of a microscope can $NOT$ be increased by

What minimum separation between two objects a human eye would be able to resolve, if the eye pupil diameter is $2 \,mm$ and the two objects are $20 \,m$ away from the eye (in $\,mm$)?
(Assume, human eye to be equivalent to a convex lens and consider the average wavelength of light as $600 \,nm$.)

The diameter of the objective of a telescope is $200 \text{ cm}$. What is the resolving power of the telescope? Take the wavelength of light $\lambda = 5000 \text{ \AA}$.