Question

Two mirrors at an angle θ produce 5 images of a point. The number of images produced when θ is decreased to θ−30 is
a.) 9
b.) 10
c.) 11
d.) 12

Answer 1

Hint: When two mirrors are placed making an angle then they reflect the images formed by each other which then again is reflected by each of the mirror until the image formed goes out of the range of the mirror. In this way multiple images are formed. We will be using the same concept here in this question.

Complete step by step solution:
The question states that there are two mirrors placed at an angle θ. Let's make a figure showing two mirrors placed at an angle θ

Now, we know that the number of images formed by any mirror is given by
$n=\dfrac{360}{\theta }-1$
But we have been given that 5 images are formed when the angle is θ
Now put this value in above equation and we get,
$5=\dfrac{360}{\theta }-1$
From this we get,
$\theta ={{60}^{\circ }}$
Now according to the question, we have to find the number of images formed at θ−30
 $60-30={{30}^{\circ }}$
So, we need to find the number of images formed at ${{30}^{\circ }}$
Now put this value in
$n=\dfrac{360}{\theta }-1$
$n=\dfrac{360}{30}-1$
n = 11
Therefore, 11 images will be formed when the mirrors are placed at an angle ${{30}^{\circ }}$
Hence, we can conclude that option (c) will be the correct answer.

Note: Here, in this question we have been given two mirrors are placed but they didn’t specify which type of mirror is placed and hence in such type of situation we will assume that two plane mirrors are placed making some angle to each other and these mirrors formed multiple images due to the reflection of images on the other mirror. This answer can vary if different types of mirrors are placed making an angle to each other.