The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1 = 4000\,\mathring{A}$ and $\lambda_2 = 6000\,\mathring{A}$ is

Explain the resolving power of optical instruments and explain the resolving power of telescopes.

$A$ telescope has an objective lens of $10\; m$ diameter and is situated at a distance of $1\; km$ from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is $5000\; \text{\AA}$, is of the order of:

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:

An astronaut is looking down on the Earth's surface from a space shuttle at an altitude of $400 \, km$. Assuming that the astronaut's pupil diameter is $5 \, mm$ and the wavelength of visible light is $500 \, nm$,the astronaut will be able to resolve a linear object of the size of about ........ $m$.

The aperture of the objective lens of a telescope is made large so as to