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

The resolving power of a telescope depends on

There are two white dots on a black paper separated by a distance of $1 \, mm$. They are observed by the naked eye. If the diameter of the eye lens is $3 \, mm$,what is the maximum distance between the dots and the eye so that they can be seen as separate (in $, m$)? The wavelength of light is $500 \, nm$.

Two vertical poles are at a distance of $6.28 \, m$ from each other. What should be the maximum distance of an observer from the poles to see them separately? (in $km$)

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)

Resolving power of a telescope increases when