The resolving power of a telescope whose lens has a diameter of $1.22 \ m$ for a wavelength of $5000 \ \mathring{A}$ is

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

Some distant star is to be observed by a telescope with an objective lens diameter of $a$, at an angular resolution of $3.0 \times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is $500$ nm, the minimum diameter of the objective lens of the telescope is . . . . . . cm. (nearest integer)

If the red light is replaced by blue light illuminating the object in a microscope, the resolving power of the microscope:

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

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 $\mu m$)