When the object is self-luminous,the resolving power of a microscope is given by the expression

The limit of resolution of a telescope is $3.0 \times 10^{-7} \text{ rad}$. Assuming that it is used to see the light of wavelength $525 \text{ nm}$ from a star, what should be the diameter of the objective (in $\text{ m}$)?

$A$ telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength $500 \text{ nm}$,at a resolution of $5 \times 10^{-7} \text{ radian}$. The value of $R$ is . . . . . . $\text{cm}$.

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 $\mu m$)

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 astronomical telescope has a large aperture to