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 $nm$)?

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

Wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \; \mathring{A}$ and $\lambda_2 = 5000 \; \mathring{A}$. The ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$) is:

Some distant star is to be observed by a telescope with an objective lens diameter of $a$, at an angular resolution of $3.0 \times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is $500$ nm, the minimum diameter of the objective lens of the telescope is . . . . . . cm. (nearest integer)

The limit of resolution of an oil immersion objective microscope of numerical aperture $0.8$ for light of wavelength $0.6 \mu m$ is

The value of numerical aperture of the objective lens of a microscope is $1.25$. If light of wavelength $5000\,\mathring{A}$ is used, the minimum separation between two points, to be seen as distinct, will be....$\mu m$