Question

Two mirrors at an angle ${\theta }^{\circ }$ produces $5$ images of a point. The number of images produced when $\theta$ is decreased to $\theta -{30}^{\circ }$ is then going to be

• A. $9$
• B. $10$
• C. $11$
• D. $12$

Answer 1

The correct option is C $11$

Given: the number of images $=5$
The number of images formed by two planes mirrors at an angle is given by:

$n=\frac{{360}^{\circ }}{\theta }-1$ (if $\frac{{360}^{\circ }}{\theta }$ is even or $n$ is odd)

or $n=\frac{{360}^{\circ }}{\theta }$ - $1$ (if $\frac{{360}^{\circ }}{\theta }$ is odd or $n$ is even)

So, for $5$ images formed by combination,

we have $\frac{{360}^{\circ }}{\theta }-1=5$
$\Rightarrow \theta ={60}^{\circ }$

When the angle is decreased to $\theta -{30}^{\circ }$,

i.e., $\theta {}^{\prime }=\theta -{30}^{\circ }={60}^{\circ }-{30}^{\circ }={30}^{\circ }$.

Thus, the number of images will be:

$n{}^{\prime }=\frac{{360}^{\circ }}{{30}^{\circ }}-1=11$ ($\frac{{360}^{\circ }}{\theta }$ is even)

So, option $\left(C\right)$ is correct.