Assuming the human pupil to have a radius of $0.25 \ cm$ and a comfortable viewing distance of $25 \ cm$,the minimum separation between two objects that the human eye can resolve at $500 \ nm$ wavelength is nearly: (in $\mu m$)

For a given wavelength,telescopes with large aperture objectives are used for:

$A$ man can clearly see two poles at a distance of $11 \, km$. What should be the minimum distance between the poles in $m$?

If a microscope is placed in air,the minimum separation of two objects seen as distinct is $6 \mu m$. If the same is placed in a medium of refractive index $1.5$,then the minimum separation of the two objects to be seen as distinct is: (in $\mu m$)

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 ........ $m$.

In telescopes, for a given wavelength, the objectives with large aperture are used for