The wavelengths of light used in an optical instrument are ${\lambda _1 = 4000 \ \text{\AA}}$ and ${\lambda _2 = 5000 \ \text{\AA}}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is:

$A$ telescope has an objective lens of $10\; m$ 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 $5000\; \text{\AA}$, is of the order of:

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.......$mm$.

Light of wavelength $\lambda$ is coming from a star. What is the limit of resolution of a telescope whose objective has diameter $r$?

Explain the resolving power of optical instruments and explain the resolving power of telescopes.

$A$ microscope has an objective of aperture $8 \text{ mm}$ and focal length of $5 \text{ cm}$. The minimum separation between two objects to be just resolved by the microscope is (wavelength of light used $= 5500 \text{ Å}$) (in $\mu\text{m}$)