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Q.

A circular plane mirror is placed on a table and a hemisphere of radius 10 cm is placed on it. The center of hemisphere is at the center of mirror. The minimum radius of circular mirror for which image of point object P is formed by the mirror is?

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a

12.8 cm

b

12.5 cm

c

12.7 cm

d

12.9 cm

answer is B.

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Detailed Solution

From figure, $\sin 37^{0} = \frac{h}{R}$

Question Image

$\begin{array}{l} ∴ h = R \sin 37^{0} = 10 \times \frac{3}{5} = 6 c m \\ A l s o, \cos 37^{0} = \frac{C A}{R} \\ C A = R \cos 37^{0} = 10 \times \frac{4}{5} = 8 c m \\ A n d \tan 53^{0} = \frac{h}{A B} \\ ∴ A B = \frac{h}{\tan 53^{0}} = \frac{6}{4 / 3} = \frac{18}{4} = 4.5 c m \end{array}$

Thus, minimum radius of mirror = CB

$= C A + A B = 8 + 4.5 = 12.5 c m$

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A circular plane mirror is placed on a table and a hemisphere of radius 10 cm is placed on it. The center of hemisphere is at the center of mirror. The minimum radius of circular mirror for which image of point object P is formed by the mirror is?