Question

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

Answer 1

Hint:-: If the object is placed on angle bisector of the two mirrors, then numbers of images formed of the object is given by
\[number\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}} - 1\]
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:
\[number\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}}\]

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
\[number\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}} - 1\]
Numbers of images we want is five
Let the angle between the mirrors is \[\theta \],
Putting the values we get
\[ \Rightarrow 5 = \dfrac{{360^\circ }}{\theta } - 1\]
\[ \Rightarrow 6 = \dfrac{{360^\circ }}{\theta }\]
Solving the equation for \[\theta \], we get
\[ \Rightarrow \theta = \dfrac{{360^\circ }}{6}\]
\[ \Rightarrow \theta = 60^\circ \]
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:
\[number\;of\,images = \dfrac{{360^\circ }}{{angle\;between\;mirrors}}\]
Numbers of images we want is five
Let the angle between the mirrors is \[\theta \],
Putting the values we get
\[ \Rightarrow 5 = \dfrac{{360^\circ }}{\theta }\]
Solving the equation for \[\theta \], we get
\[ \Rightarrow \theta = \dfrac{{360^\circ }}{5}\]
\[ \Rightarrow \theta = 72^\circ \]
Here to get five images of a single object , one should have a plane mirror at an angle of \[72^\circ \].
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 ( \[\theta = 0^\circ \]).
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.