Two stars are $10$ light years away from the Earth. They are seen through a telescope of objective diameter $30\, cm$. The wavelength of light is $600\, nm$. To see the stars just resolved by the telescope,the minimum distance between them should be ( $1$ light year $= 9.46 \times 10^{15}\, m$) of the order of

$A$ person is observing a bacteria through a compound microscope. For better analysis and to improve the resolving power,he should:

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 ...... $m$.

Two point white dots are $1 \ mm$ apart on a black paper. They are viewed by an eye with a pupil diameter of $3 \ mm$. Approximately,what is the maximum distance at which the dots can be resolved by the eye? (Take wavelength of light $= 500 \ nm$)

We use a simple microscope to magnify an object. The microscope has a numerical aperture of $\sin \alpha = 0.24$. The object is so small that the resolving power of the microscope is fully utilized. If the diameter of the eye's pupil is $d = 4.0 \ mm$ and the least distance of distinct vision is $D = 25 \ cm$,what is the minimum magnifying power of the microscope?

Assume that light of wavelength $6000\,\mathring{A}$ is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of $100\,\text{inch}$?