Light of wavelength $\lambda$ is coming from a star. What is the limit of resolution of a telescope whose objective has diameter $r$?

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

Two luminous point sources separated by a certain distance are at $10 \,km$ from an observer. If the aperture of his eye is $2.5 \times 10^{-3} \,m$ and the wavelength of light used is $500 \,nm$, the distance of separation between the point sources just seen to be resolved is (in $\,m$)

According to Abbe,in the formula for the resolving power of a microscope,the numerical aperture is represented by:

Assertion : $A$ famous painting was painted by not using brush strokes in the usual manner,but rather a myriad of small colour dots. In this painting the colour you see at any given place on the painting changes as you move away.
Reason : The angular separation of adjacent dots changes with the distance from the painting.

An astronomical telescope has a large aperture to