Question

What is the multiple reflection of light? How many images are formed when the angle between the two mirrors is $60^\circ $ and $45^\circ $ ?

Answer 1

Hint:In order to solve this question we need to understand reflection and number of images. So reflection is defined as a phenomenon of light in which we get the light in the same medium after striking a surface. There are two types of reflection, one is diffused and other is regular reflection. Diffused reflection is one in which light is reflected from a rough surface and regular reflection is one in which light is reflected from a smooth surface. So when two plane mirrors are at some angle with each other, then light suffers multiple reflections back and forth, so more than one image is formed.

Complete step by step answer:
Multiple reflection means reflection from various regular surfaces like if we place the two mirrors at some angle with each other than light reflected from more than one surface, this is an example of multiple reflection.

Consider two plane mirrors at an angle of $\theta $ with each other.So by multiple reflection formula:
$n = \dfrac{{360^\circ }}{\theta } \to (i)$
Here, “$n$” is integer.
If $n$ is even integer then number of images formed is $I = n - 1$
If $n$ is odd integer then number of images formed is $I' = n$

So according question, first $\theta = 60^\circ $
So “n” would be,
$n = \dfrac{{360}}{{60}}$ from equation (i)
$\Rightarrow n = 6$
Since “n” is even, so number of images formed is,
$I = n - 1$
Putting values we get,
$I = 6 - 1$
$\therefore I = 5$

Second $\theta = 45^\circ $
So “n” would be,
$n = \dfrac{{360}}{{45}}$ from equation (i)
$\Rightarrow n = 8$
Since “n” is even, so number of images formed is,
$I = n - 1$
Putting values we get,
$I = 8 - 1$
$\therefore I = 7$

Hence, the number of images formed when the angle between the two mirrors is $60^\circ $ and $45^\circ$ are 5 and 7.

Note: It should be remembered that, here we have taken one less than calculated value for “n” to be even because if “n” is even then out of images formed, one image is formed at object location itself, so we have to count one less than value of “n”. Also we are able to view the world due to diffused reflection.