$A$ telescope has a large diameter of the objective. Then,its resolving power is

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 $mm$)

The diameter of the objective lens of a telescope is $5.0\, m$ and the wavelength of light is $6000\ \mathring{A}$. The limit of resolution of this telescope will be......$sec$.

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 $............. \, \mu m$.

The diameter of the objective of a telescope is $10 \, cm$. There are two objects at a distance of $1 \, km$ from it. What should be the minimum distance between these two objects so that their images are seen as separate by this telescope? The wavelength of light is $5000 \, \mathring{A}$.

Some distant star is to be observed by a telescope with an objective lens diameter of $a$, at an angular resolution of $3.0 \times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is $500$ nm, the minimum diameter of the objective lens of the telescope is . . . . . . cm. (nearest integer)