Q. A telescope has an objective lens of $10\ cm$ diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is $5000\ \mathring{\mathrm{A}}$, is of the order of
A) 0.5 $m$
B) 5 $m$
C) 5 $mm$
D) $5\ cm$
Explanation
(c) $\theta = \frac{x}{d} = \frac{1.22\ \lambda}{a}$
$\Rightarrow x = \frac{1.22\ \lambda d}{a}$
$= \frac{1.22 \times 5000 \times 10^{- 10} \times 10^{3}}{10 \times 10^{- 2}} = 6.1\ mm$
$i.e.,$ order will be $5\ mm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.