The limit of resolution of a telescope is $3.0 \times 10^{-7} \text{ rad}$. Assuming that it is used to see the light of wavelength $525 \text{ nm}$ from a star, what should be the diameter of the objective (in $\text{ m}$)?

The diameter of the objective lens of a microscope makes an angle $\beta$ at the focus of the microscope. Further,the medium between the object and the lens is an oil of refractive index $n$. Then the resolving power of the microscope

The aperture of the objective lens of a telescope is made large so as to

Assertion: The resolving power of a telescope is more if the diameter of the objective lens is more.
Reason: Objective lens of large diameter collects more light.

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 distance of the moon from earth is $3.8 \times 10^5 \text{ km}$. The eye is most sensitive to light of wavelength $5500 \text{ Å}$. The separation of two points on the moon that can be resolved by a $500 \text{ cm}$ telescope will be......$m$.