Question 141 of 191

The aperture diameter of a telescope is $5m$ . The separation between the moon and the earth is $4\times {10}^{5}km$ . With light of wavelength of $5500Å$ , the minimum separation between objects on the surface of moon, so that they are just resolved, is close to:

A$60m$B$20m$C$200m$D$600m$

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Answer: (A) $60m$

$\theta =1.22\dfrac{\lambda }{a}$
Distance $={O}_{1}{O}_{2}=d\theta$
$=1.22\dfrac{\lambda }{a}d$
Distance $={O}_{1}{O}_{2}=\dfrac{1.22\times 5893\times {10}^{-10}\times 4\times {10}^{8}}{5}\approx 57.5m$
$∴$ answer from options $=60m$
(minimum distance)