Question

Three plane mirrors are kept as shown in the figure. A point object $O$ is kept at the centroid of the equilateral triangle. Which of the following statements is/are true.

• A. Total number of images formed by three mirror system is $12$.
• B. All the images formed by the plane mirrors $AB$ and $BC$ and object lie on the periphery of circle centred at $B$.
• C. Number of images formed by any two mirrors in the given three mirror system is equal to $4$.
• D. Number of images formed by any two mirrors in the given three mirror system is equal to $5$.

Answer 1

Answer: (A), (B), (D)

Number of images formed by any two mirrors in the given three mirror system is equal to $5$.

Let $A$ $B$ and $C$ be the vertices of the equilateral triangle formed by three mirrors $AB$ ,$BC$ and $CA$.

From the diagram we can deduce that, angle between any two mirrors is ${60}^{\circ }$.

To find the number of images formed by any two mirror system ,
We find, $\frac{360}{\theta }=\frac{360}{60}=6$ (even number)

$\therefore$ Number of images formed by any two plane mirrors in given system , $n=(\frac{360}{\theta }-1)=6-1=5$

All these images along with the object are concylic.

For a two mirror system $AB$ and $BC$, all images and objects lie on the periphery of a circle centred at $B$ and having radius $BO$.

Similarly, for the system $AB$ and $AC$.


When we draw a circles with radius $AO$ , $BO$ and $CO$. They coincide with each other at three points.

From the figure, points $4$ , $8$ and $12$ are the points where the images are coinciding.

$\Rightarrow$ Total no of images = $3\times$ Number of images on each circle - Total number of coinciding images = $(3\times 5)-3=12$

Hence, options (a) , (b) and (d) are the correct answers.

Caution :- Care must be taken while counting the total number of images formed by the system of $3$ mirrors.