First slide

Plane mirror

Question

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?

Easy

A

12.8 cm
B

12.5 cm
C

12.7 cm
D

12.9 cm

Solution

From figure, $\sin 37^{0} = \frac{h}{R}$
$\begin{array}{l} ∴ h = R \sin 37^{0} = 10 \times \frac{3}{5} = 6 c m \\ A l s o, \cos 37^{0} = \frac{C A}{R} \\ C A = R \cos 37^{0} = 10 \times \frac{4}{5} = 8 c m \\ A n d \tan 53^{0} = \frac{h}{A B} \\ ∴ A B = \frac{h}{\tan 53^{0}} = \frac{6}{4 / 3} = \frac{18}{4} = 4.5 c m \end{array}$
Thus, minimum radius of mirror = CB
$= C A + A B = 8 + 4.5 = 12.5 c m$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App