Question

How many images of himself can an observer see if two adjacent walls and the ceiling of a rectangular room are mirror surfaced?

• A. $2$
• B. $3$
• C. $5$
• D. $7$

Answer 1

The correct option is D

$7$

Step 1: Image formed by the adjacent walls

We know that the number of images formed by two mirrors inclined towards each other at an angle $\theta$ is given by

$n=\frac{360}{\theta }-1$

In the question, it is given that the two adjacent walls are of a rectangular room.

We know that all the angles of a rectangle are $90°$.

Hence $\theta =90°$

Therefore, the number of images formed by these two adjacent walls,

$n=\frac{360}{90}-1$

$=4-1$

$=3$

Step 2: Image formed by the ceiling

Again, there is a mirror on the ceiling as well.

The wall and the ceiling mirror also are inclined toward each other at $90°$.

Therefore, the number of images formed in this case,

$n=\frac{360}{\theta }-1$

$=\frac{360}{90}-1$

$=4-1$

$=3$

Step 3: Total number of images formed

Apart from this, the observer himself also has his image formed on the ceiling.

Therefore there will again be one extra image.

Hence the total number of images formed is,

$3+3+1=7$ images.

Hence, in the room, $7$ images are formed and therefore, option (D) is the correct answer.