Question

A bulb is placed between two plane mirrors at an angle of ${60^0}$ .What is the number of images formed ?
A) 5
B) 6
C) 4
D) 3

Answer 1

Hint:Number of images formed by the object kept between two plane mirrors at a certain angle is always odd and can be found using the respective formula for the number of images by two mirrors at a certain angle.

Complete step by step answer:
The number of images formed between two mirrors at certain angles is given by the formulas:
$n = \dfrac{{{{360}^0}}}{\theta }$ __________ (1)
$n = \dfrac{{{{360}^0}}}{\theta } - 1$ __________ (2)
Where,
n is the number of images formed
And $\theta $ is the angle between the two mirrors.
Here, we have to try both the formulas and whichever formula gives ‘n’ as an odd number will be the required answer.
Here in this problem angle between the two mirrors is 60° (Given)
$\therefore \theta = {60^ \circ }$
First we substitute this value of $\theta $ in (1):
$n = \dfrac{{{{360}^0}}}{\theta }$
$n = \dfrac{{{{360}^0}}}{{{{60}^0}}} = 6$
n=6 , which is even number and hence we cannot consider it and we go for eqn (2):
$n = \dfrac{{{{360}^0}}}{\theta } - 1$
(substituting the value of $\theta $= ${60^0}$)
$n = \dfrac{{{{360}^0}}}{{{{60}^0}}} - 1 = 6 - 1 = 5$
n=5 which is an odd number so, we have to consider this as the answer.
Therefore, when a bulb is placed between two plane mirrors at an angle of ${60^0}$ the number of images formed is 5 and hence the correct option is A)

Note:In actuality, the number of images formed are even, but the last two images that are formed coincide (fall on one another) with each other and appear to be single images and hence are not considered as two separate images. Thus we can say that the images formed between two mirrors will always be odd in number