Two points separated by a distance of $0.1 \, mm$ can just be resolved in a microscope when a light of wavelength $6000 \, Å$ is used. If the light of wavelength $4800 \, Å$ is used, this limit of resolution becomes: (in $mm$)

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 $\text{ cm}$)

In an optical instrument,the wavelengths of light used are $\lambda_1 = 4000 \ \mathring{A}$ and $\lambda_2 = 5000 \ \mathring{A}$. What is the ratio of their resolving powers?

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: An electron microscope can achieve better resolving power than an optical microscope.
Reason $R$: The de Broglie wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light.
In the light of the above statements, choose the correct answer from the options given below:

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

Resolving power of a microscope can $NOT$ be increased by