Which of the following is the smallest size grain that can be seen using a normal microscope using visible light $(400 \ nm < \lambda < 700 \ nm)$ (in $nm$)?

Our eye is most sensitive for which of the following wavelengths in $\mathring{A}$?

The limit of resolution of a telescope is $2.5 \times 10^{-7} \text{ rad}$. If the telescope is used to detect light of wavelength $500 \text{ nm}$ coming from a star, the diameter of the objective lens used by the telescope is: (in $\text{ cm}$)

The diameter of the objective lens of a telescope is $250\, cm$. For light of wavelength $600\, nm$ coming from a distant object, the limit of resolution of the telescope is close to:

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 $\frac{a}{1.22 \lambda}$.

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