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Question: Question:- To get five images of a single object , one should have a plane mirror at an angle of .. ...

Question:- To get five images of a single object , one should have a plane mirror at an angle of ..
A. 30∘30^\circ
B. 72∘72^\circ
C. 90∘90^\circ
D. 150∘150^\circ

Explanation

Solution

Hint:- : If the object is placed on angle bisector of the two mirrors, then numbers of images formed of the object is given by
number  of images=360∘angle  between  mirrors−1number\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}} - 1
The number of images may be odd or even both.
And if the object is not placed on angle bisector of the two mirrors & the numbers of images formed of the object is odd in numbers , then we have:
number  of images=360∘angle  between  mirrorsnumber\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}}

Complete step-by-step solution :We want the numbers of images to be five
Case (1) : - If the object is placed at angle bisector of the mirrors
number  of images=360∘angle  between  mirrors−1number\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}} - 1
Numbers of images we want is five
Let the angle between the mirrors is θ\theta ,
Putting the values we get
⇒5=360∘θ−1\Rightarrow 5 = \dfrac{{360^\circ }}{\theta } - 1
⇒6=360∘θ\Rightarrow 6 = \dfrac{{360^\circ }}{\theta }
Solving the equation for θ\theta , we get
⇒θ=360∘6\Rightarrow \theta = \dfrac{{360^\circ }}{6}
⇒θ=60∘\Rightarrow \theta = 60^\circ
Here no option matches with the result which we have obtained , so we are going for case ( 2 ).
Case (2) : - If the object is not placed at angle bisector of the mirrors & , the numbers of images formed of the object is odd, then we have:
number  of images=360∘angle  between  mirrorsnumber\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}}
Numbers of images we want is five
Let the angle between the mirrors is θ\theta ,
Putting the values we get
⇒5=360∘θ\Rightarrow 5 = \dfrac{{360^\circ }}{\theta }
Solving the equation for θ\theta , we get
⇒θ=360∘5\Rightarrow \theta = \dfrac{{360^\circ }}{5}
⇒θ=72∘\Rightarrow \theta = 72^\circ
Here to get five images of a single object , one should have a plane mirror at an angle of 72∘72^\circ .
Hence option ( B ) is the correct answer.

Note:-
If we want to find an infinite number of images of an object, place both of the mirrors parallel, that means the angle between them is ( θ=0∘\theta = 0^\circ ).
If a plane mirror is placed in front of an object and the object approaches the mirror with velocity ( v ), then the velocity of its image will appear to be ( 2v ) in the mirror.