Question

A source of light lies on the angle bisector of two plane mirrors inclined at an angle $\theta $. The value of $\theta $, so that the light reflected from one mirror does not reach the other mirror will be:
A. $\theta \geqslant {120^ \circ }$
B. $\theta > {90^ \circ }$
C. $\theta \leqslant {120^ \circ }$
C. None of the above

Answer 1

Hint It is given in the question that the light reflected from one mirror does not reach the other mirror, so we can determine from here that the number of images formed in this system must not be greater than two. Replacing this value in the appropriate formula we get the condition for the angle.
Formula used
$n = \dfrac{{{{360}^ \circ }}}{\theta } - 1$ where $n$ is the number of images formed when two plane mirrors are inclined at an angle $\theta $

Complete step by step answer
When light is incident on a plane mirror, it leads to the following observation:
The incident ray, the normal at the point of incidence and the reflected ray all lie in the same plane.
The angle of reflection is equal to the angle of incidence.
These observations are termed as the ‘laws of reflection’
Now, let us consider two plane mirrors who are inclined such that they make an angle of \[\theta \] with one another.
Since it's given that the light reflected from one mirror does not reach the other, the number of images formed must not be greater than two.
So we have $n \leqslant 2$
Now the formula for the number of images formed is given as
$n = \dfrac{{{{360}^ \circ }}}{\theta } - 1$
So equation these two equations we get,
$\dfrac{{{{360}^ \circ }}}{\theta } - 1 \leqslant 2$ where $\theta $ is the angle between the two inclined mirrors.
$
   \Rightarrow \dfrac{{{{360}^ \circ }}}{\theta } \leqslant 3 \\
   \Rightarrow \theta \geqslant \dfrac{{{{360}^ \circ }}}{3} \\
   \Rightarrow \theta \geqslant {120^ \circ } \\
$
So the condition for which the light reflected from one mirror does not reach the other mirror is $\theta \geqslant {120^ \circ }$

Therefore, the correct answer is A.


Note Apart from plane mirrors, there are also spherical mirrors of two types-convex and concave. A concave mirror is one whose reflecting surface is towards the centre of the sphere of which the mirror is a part of. A convex mirror is one whose reflecting surface is away from the centre of the sphere of which the mirror is a part.