The correct relation between limit of resolution and resolving power is

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 $500 \, nm$.

The average distance between the earth and moon is $38.6 \times 10^4 \ km$. The minimum separation between the two points on the surface of the moon that can be resolved by a telescope whose objective lens has a diameter of $5 \ m$ with $\lambda = 6000 \ \mathring{A}$ is ...... $m$.

In an optical instrument,the wavelengths of light used are $\lambda_1 = 4000 \ \mathring{A}$ and $\lambda_2 = 5000 \ \mathring{A}$. What is the ratio of their resolving powers?

The separation between two microscopic particles is measured as $P_A$ and $P_B$ by two different lights of wavelength $2000 \; \mathring{A}$ and $3000 \; \mathring{A}$ respectively. Then:

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