Two points separated by a distance of $0.1\,mm$ can just be resolved in a microscope when a light of wavelength $6000\ \mathring{A}$ is used. If the light of wavelength $4800\ \mathring{A}$ is used,this limit of resolution becomes.......$mm$.

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)

How to increase the resolving power of a telescope and a microscope?

Two points separated by a distance of $0.1 \, mm$ can just be resolved in a microscope when a light of wavelength $6000 \, Å$ is used. If the light of wavelength $4800 \, Å$ is used, this limit of resolution becomes: (in $mm$)

Two vertical poles are at a distance of $6.28 \, m$ from each other. What should be the maximum distance of an observer from the poles to see them separately? (in $km$)

$A$ telescope has an objective lens of $10\, cm$ 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 $5000\,\mathring{A}$,is the order of