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Question: To get three images of a single object, one should have two plane mirrors at an angle of: A. \(60^...

To get three images of a single object, one should have two plane mirrors at an angle of:
A. 60∘60^\circ
B. 90∘90^\circ
C. 120∘120^\circ
D. 30∘30^\circ

Explanation

Solution

here, in the above example we are using two plane mirrors to get three images of a single object. A plane mirror is a mirror that consists of a flat surface that is used to reflect the light and form an image. The number images formed by an object will depend upon the angle between the plane mirrors.

FORMULA USED: The formula used for calculating the angle between two plane mirrors to get number of images of a single object is given by
n=360∘θ−1n = \dfrac{{360^\circ }}{\theta } - 1
Here, nn is the number of images formed by a mirror and θ\theta is the angle between the mirrors to get nn number of images.

COMPLETE STEP BY STEP ANSWER:
Here, in the above example, we are given three images of a single object. We can say that the number of placement of mirrors will decide the number of images of an object.
Now, the formula used for calculating the number of images of an object formed by two plane mirror can be calculated by the given formula
n=360∘θ−1n = \dfrac{{360^\circ }}{\theta } - 1
Now, it is given in the question that the there are three images of a single object, therefore, number of images, n=3n = 3
Therefore, the above equation becomes
3=360∘θ−13 = \dfrac{{360^\circ }}{\theta } - 1
⇒ 3+1=360∘θ\Rightarrow \,3 + 1 = \dfrac{{360^\circ }}{\theta }
⇒ 4=360∘θ\Rightarrow \,4 = \dfrac{{360^\circ }}{\theta }

⇒ θ=360∘4 \Rightarrow \,\theta = \dfrac{{360^\circ }}{4}
⇒ θ=90∘\Rightarrow \,\theta = 90^\circ
Therefore, to get three images of a single object, one should place two plane mirrors at an angle of 90∘90^\circ

Hence, option (B) is the correct option.
NOTE: To obtain images of an object the angle between the mirrors should be less than or equal to 120∘120^\circ and greater than or equal to 90∘90^\circ . Also, to obtain two or more than two images of an object, the angle between the mirrors should be less than or equal to 90∘90^\circ . That is why, in the above example, we got the answer 90∘90^\circ .