Question

Two plane mirrors are initially inclined at 30° and they are moved apart by 30° each time, till the angle between them becomes 120°. If an object is placed symmetrically between them then find the sum of all the images formed.

• A. 20
• B. 21
• C. 22
• D. 23

Answer 1

The correct option is

C

21

Here number of images formed during each occassion is noted and added

Number of images formed = n = $(\frac{{360}^{\circ }}{\theta }-1)$

Total number of images = Number of images when angle between mirrors is at 30°, 60°, 90° and 120°

n = $(\frac{{360}^{\circ }}{{30}^{\circ }}-1)$ + $(\frac{{360}^{\circ }}{{60}^{\circ }}-1)$ + $(\frac{{360}^{\circ }}{{90}^{\circ }}-1)$ + $\left(\frac{{360}^{\circ }}{{120}^{\circ }}\right)$

n = 11 + 5 + 3 + (3-1) = 21

Note: As the object is placed symmetrically