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Q.

Find the diameter of the image of the moon formed by a spherical concave mirror of focal length 7.6 m. The diameter of the moon is 3450 km and the distance between the earth and the moon is $3.8 \times 10^{5} km$ .

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a

5.8 cm

b

4.5 cm

c

6.9 cm

d

5.6 cm

answer is D.

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Detailed Solution

$\begin{array}{l} f = - 7 .6 \\ u = - 3 .8 \times 10^{5} \\ \frac{1}{v} = \frac{- 1}{7 .6} + \frac{1}{3 .8 \times 10^{5}} \\ = \frac{- 3 .8 \times 10^{5} - 7 .6}{3 .8 \times 7 .6 \times 10^{5}} \\ v = - 7 .6 m \\ h^{1} = \frac{- 7 .6}{3 .6 \times 10^{5}} \times 3450 = 6 .9 cm \end{array}$

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