Large apertures of telescopes are used for

Calculate the limit of resolution of a telescope objective having a diameter of $200\, cm$, if it has to detect light of wavelength $500\, nm$ coming from a star.

Resolving power of a microscope can $NOT$ be increased by

At Kavalur in India,astronomers using a telescope whose objective had a diameter of $1 \, m$ started using a telescope of diameter $2.54 \, m$. This resulted in:

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

$A$ telescope is used to observe two objects at a distance of $z = 10 \ km$ which are $s = 0.12 \ m$ apart and illuminated by light of wavelength $\lambda = 600 \ nm$. Estimate the diameter of the objective lens of the telescope if it can just resolve the two objects. Assume diameter $D >> \lambda$ and separation between objects $s << z$. The answer is in $cm$.