Question

# A telescope of aperture diameter $5m$ is used to observe the moon from the earth. Distance between the moon and earth is $4×{10}^{5}km$. The minimum distance between two points on the moon’s surface which can be resolved using this telescope is close to (Wavelength of light is $5500\stackrel{\circ }{A}$)

A

$60m$

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B

$20m$

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C

$600m$

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D

$200m$

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Solution

## The correct option is A $60m$Step 1. Given Data:Diameter of the aperture, $D=5m$Distance between the moon and the earth, $d=4×{10}^{8}m$Wavelength, $\lambda =5500×{10}^{-10}m$Let the minimum distance between two points on the moon’s surface be $s$.Step 2. Minimum angle, $\theta$ for clear resolution:$\theta =1.22\left(\frac{\lambda }{D}\right)\dots \left(1\right)\phantom{\rule{0ex}{0ex}}s=d\theta \phantom{\rule{0ex}{0ex}}\theta =\frac{s}{d}\dots \left(2\right)$ Step 3: Calculating the minimum distance between two points, $s$Equating equation $\left(1\right)$ and equation $\left(2\right)$,$\frac{s}{d}=1.22\left(\frac{\lambda }{D}\right)\phantom{\rule{0ex}{0ex}}\frac{s}{4×{10}^{8}}=\frac{1.22×5500×{10}^{-10}}{5}\phantom{\rule{0ex}{0ex}}s=53.68m$Nearest option is $60m$Hence, the correct option is (A).

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