Question

For the arrangement of plane mirrors as shown in the figure where the length of the mirrors $M_1$ and $M_2$ are equal, find the number of images formed if a point object $O$ is placed at the centroidal position.

• A. $21$
• B. $14$
• C. $17$
• D. $24$

Answer 1

The correct option is A $21$

There are three pairs of plane mirror.
Angle between pair $M_1$ and $M_2$,
${\theta }_1={120}^{\circ }$
So, $n_1=\frac{{360}^{\circ }}{\theta }=\frac{{360}^{\circ }}{{120}^{\circ }}=3$
As $n$ is odd and object is placed symmetrical, so the number of images formed $=n-1=3-1=2$
Angle between pairs $M_2$ and $M_3$ and $M_3$ and $M_1$,
${\theta }_2={30}^{\circ }$
[from concept of geometry, isosceles triangle is formed]
So, $n_2=\frac{{360}^{\circ }}{\theta }=\frac{{360}^{\circ }}{{30}^{\circ }}=12$
As $n$ is even, so the number of images formed by each pair$=n-1=12-1=11$
We subtract the number of plane mirrors from the total number of images obtained by superposition.
So, total number of images formed,
$N=2+2\times 11-3=21$