$A$ microscope objective gathers light over a cone of semi-vertex $30^o$ and uses visible light of wavelength $5500 \text{ Å}$. Its resolving limit is

The resolving limit of a healthy human eye is about:

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.

If the numerical aperture $(NA)$ of a microscope is increased,then its:

Assertion $(A):$ To increase the resolving power of a telescope,the aperture $(a)$ of the objective lens should be large.
Reason $(R):$ The resolving power of a telescope is given by $\frac{a}{1.22 \lambda}$.

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