Large apertures of telescopes are used for

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

$A$ 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

The separation between two microscopic particles is measured as $P_A$ and $P_B$ by two different lights of wavelength $2000 \; \mathring{A}$ and $3000 \; \mathring{A}$ respectively. Then:

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

$A$ telescope of diameter $2 \ m$ uses light of wavelength $5000 \ \mathring{A}$ for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is