If $f_{0} = 5 \, cm$,$\lambda = 6000 \, \mathring{A}$,and $a = 1 \, cm$ for a microscope,what will be its resolving power?

$A$ telescope of diameter $2 \ m$ uses light of wavelength $5000 \ \mathring{A}$ for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is

The resolving power of a compound microscope will be maximum when

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:

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:

When the wavelengths of light used in optical instruments $A$ and $B$ are $4500 \, \text{Å}$ and $6000 \, \text{Å}$ respectively, the ratio of the resolving power of $A$ to $B$ will be: