Question

Two plane mirrors are placed making an angle \[\theta \] in between them. What is the expression for the number of images formed of an object placed between the mirrors?
A. n if n = $\dfrac{{{{360}^0}}}{\theta }$ is odd and the object is asymmetrically placed.
B. n – 1 if n = $\dfrac{{{{360}^0}}}{\theta }$ is even, or odd and object is symmetrically placed.
C. Both A and B.
D. None.

Answer 1

Hint: We should note the principle of image creation of an object by a mirror plane to solve this problem. The amount of image that is created depends on the angle between the two mirrors.

Complete step-by-step solution -
We found that when an object is positioned between two plane mirrors that create an angle \[\theta \] between them, multiple images of that object can be seen in the mirrors. This is because, for the second mirror, the image in the first mirror acts as an object and for the first mirror the image in the second mirror acts as an object. This phenomenon is continuing and we can see several images of one object.
Now, the number of images produced by an object positioned between two mirrors must be identified. The number of pictures of an object if two plane mirrors is inclined at an angle, then the number of pictures given by
   $\Rightarrow$ n = $\dfrac{{{{360}^0}}}{\theta } - 1$, if the integer $\dfrac{{{{360}^0}}}{\theta }$ is even
   $\Rightarrow$ n = $\dfrac{{{{360}^0}}}{\theta } - 1$, if the target $\dfrac{{{{360}^0}}}{\theta }$ is an odd integer and lies on the angle bisector (symmetrically) and
   $\Rightarrow$ n = $\dfrac{{{{360}^0}}}{\theta }$, if $\dfrac{{{{360}^0}}}{\theta }$ is an odd integer and the point is not (asymmetrically) on the angle bisector.
Therefore option (C) is the right alternative.

Note: If we ask these questions, we must note that if an object is positioned in front of a plane mirror, only one image of the object is created, but if the object image is viewed in two plane mirrors that are inclined to each other by an angle, then more than one image is formed.