Question

A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of ${300}^{\circ }$. The number of observable images are
(Formula for number of images is $\frac{360}{\theta }-1$, where $\theta$ is the angle between the mirrors.)

• A. $15$
• B. $12$
• C. $11$
• D. $13$

Answer 1

The correct option is C $11$

Given:
Angle of deviation, $\delta ={300}^{\circ }$
We know that, the angle of deviation when the ray is successively reflected by two plane mirrors is given by,
$\delta ={360}^{\circ }-2\theta$, where $\theta$ is the angle between the mirrors.
$\Rightarrow {300}^{\circ }={360}^{\circ }-2\theta$
$\Rightarrow \theta =\frac{{360}^{\circ }-{300}^{\circ }}{2}={30}^{\circ }$
${30}^{\circ }$ is the angle at which both mirrors are inclined.
So,
$n=\frac{{360}^{\circ }}{\theta }=\frac{{360}^{\circ }}{{30}^{\circ }}=12$
As $n$ is even, hence, the number of images,
$=n-1=12-1=11$