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:

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

An astronomical telescope has a large aperture to

Two points separated by $0.05 \, mm$ can just be inspected in a microscope when light of wavelength $6000 \, \mathring{A}$ is used. If light of wavelength $3000 \, \mathring{A}$ is used,then the limit of resolution becomes ........... $mm$.

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:

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: