Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# 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. $150^\circ$

Last updated date: 21st Jun 2024
Total views: 404.4k
Views today: 7.04k
Verified
404.4k+ views
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.