Q. Two stars are situated at a distance of 8 light year from the earth. These are to be just resolved by a telescope of diameter 0.25 m. If the wavelength of light used is $5000\mathring{\mathrm{A}}$, then the distance between the stars must be
A) $3 \times 10^{10}\ m$
B) $3.35 \times 10^{11}\ m$
C) $1.95 \times 10^{11}\ m$
D) $4.32 \times 10^{10}\ m$
Explanation
(c) Limit of resolution of the telescope
$a = \frac{1.22\lambda}{a} = \frac{d}{x}$
Or $d = \frac{1.22\lambda\ x}{a}$
$= \frac{1.22 \times 5 \times 10^{- 7} \times 8 \times 10^{16}}{0.25} = 1.95 \times 10^{11}m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.