Question

A telescope has an objective lens of $20\text{cm}$ diameter and is situated at a distance of $2\text{km}$ from two objects. The minimum distance between the two objects, which can be resolved by the telescope, when mean wavelength of light is $6000\text{Å}$, is order of

• A. $7\text{m}$
• B. $7\text{cm}$
• C. $7\text{mm}$
• D. $7\text{km}$

Answer 1

The correct option is C $7\text{mm}$

Limit of resolution of telescope $=\frac{1.22\lambda }{D}$

$\frac{X}{2000}=\frac{1.22\lambda }{D}$

$X=\frac{1.22(6\times {10}^{-7})2\times {10}^3}{20\times {10}^{-2}}$

$X=6\times 1.22\times {10}^{-3}$

$X=7.32\times {10}^{-3}$

$X$ is order of $7\text{mm}$