Question

State the number of images of an object placed between two mirrors, formed in each case when mirrors are inclined to each other at (a) ${90^ \circ }$ and (b) ${60^ \circ }$.

Answer 1

Hint: Define the formation of an image in a mirror. If two plane mirrors are inclined to each other, find the mathematical expression for the number of images produced. The number of images generated is determined by the angle between the mirror and the object's position in relation to it.

Complete step-by-step solution:
More than one image is created when two plane mirrors are inclined at an angle to each other. The angle between the two mirrors and the position of the object between the two mirrors determine the number of images produced.
The number of images created is if the angle between the mirrors is $\theta $.
$n = (\dfrac{{{{360}^ \circ }}}{\theta }) - 1,when(\dfrac{{{{360}^ \circ }}}{\theta })$ is an even integer.
If $\left( {\dfrac{{{{360}^ \circ }}}{\theta }} \right)$is an odd number, the number of images produced is determined by the object's location between the mirrors. The number of images produced would be $n = \left( {\dfrac{{{{360}^ \circ }}}{\theta }} \right) - 1$if the object is symmetrically positioned between the mirrors. The number of images created when the object is positioned asymmetrically between the mirrors is $\left( {\dfrac{{{{360}^ \circ }}}{\theta }} \right)$ .
So, now
(a). The first angle is ${90^ \circ }$
  $\therefore $ Number of images formed
   $ = \dfrac{{360}}{{90}} - 1 \\
   = 4 - 1 \\$
So, the number of images will be 3.
(b). The second angle is ${60^ \circ }$
   $\therefore $Number of images formed
$ = \dfrac{{360}}{{60}} - 1 \\
   = 6 - 1 \\
   = 5 \\ $
So, the number of images will be 5.

Note: Let us talk about one more case when two mirrors are placed parallel to each other which is a very known one. When two plane mirrors are positioned parallel to each other, no matter how far apart, infinite images are created.