question_answer

The aperture diameter of a telescope is 5 m. The separation between the moon and the earth is\[4\times {{10}^{5}}\text{ }km\]. With light of wavelength of 5500\[\overset{\text{o}}{\mathop{\text{A}}}\,\], the minimum separation between objects on the surface of moon, so that they are just resolved, is close to: [JEE MAIN Held on 09-01-2020 Morning]

A) 20 m

B) 200 m

C) 600 m

D) 60 m

Correct Answer: D

Solution :

[d]

\[\theta =1.22\frac{\lambda }{a}\]

Distance \[{{O}_{1}}{{O}_{2}}=\left( \theta  \right)d\]

\[=\left( 1.22\frac{\lambda }{a} \right)d\]

\[=\frac{\left( 1.22 \right)\left( 5500\times {{10}^{-10}} \right)\times 4\times {{10}^{5}}\times {{10}^{3}}}{5}\]

\[=5368\times {{10}^{-2}}m\]

\[=53.68m\]