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A person is in a room whose ceiling and two adjacent walls are mirrors. How many images are formed:
A) $5$
B) $6$
C) $7$
D) $8$

seo-qna
Last updated date: 20th Jun 2024
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Answer
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Hint:- The total number of the angle around a point will be ${360^0}$ . The angle of inclination is divided from this angle. And one is subtracted will give the number of images formed by two mirrors. We have to consider the ceiling mirror also for the final answer.

Complete Step by step answer:
In a plane mirror the incident ray will be reflected in an angle. The angle of incidence and the reflection will be equal.
The expression for finding the number of images formed when two mirrors are inclined is given by,
$\Rightarrow n = \dfrac{{{{360}^\circ }}}{\theta } - 1$
Where, $\theta $ is the angle of inclination of the two mirrors.
We have given that in a room ceiling and two adjacent walls are mirrors. The two adjacent mirrors are inclined at an angle of ${90^\circ }$ . Therefore the total images formed by the two images are given by,
$\Rightarrow \dfrac{360^\circ}{90^\circ}-1$
$=4-1$
$=3$
Thus the total images formed by the two adjacent walls is $3$ .
We have the ceiling of the room as a mirror. Therefore the three images and the person itself are objects to the mirror in the ceiling.
Therefore, the total images will be $3 + 1 = 4$ .
Hence the total number of images is $4 + 3 = 7$
Therefore in the room $7$ images are formed.

The answer is option C.

Note: The three mutually perpendicular mirrors will always form seven images. And two perpendicular mirrors will always form three images. Infinite images will form if there is no angle between the mirrors.