Question

Two mirrors placed at an angle of $\theta$ produces $5$ images of an object placed symmetrically between the mirrors. The number of images produced when $\theta$ is decreased by ${30}^{\circ }$ will be

• A. $14$
• B. $13$
• C. $11$
• D. $12$

Answer 1

The correct option is C $11$

Initially, number of images produced $=5$
$\Rightarrow n-1=5$ (symmetrical)
$\Rightarrow n=5+1=6$
or, $\frac{{360}^{\circ }}{\theta }=6$
$\therefore \theta =\frac{{360}^{\circ }}{6}={60}^{\circ }$
Now, $\theta$ is decreased by ${30}^{\circ }$
So, ${\theta }^{{}^{\prime }}=\theta -{30}^{\circ }={60}^{\circ }-{30}^{\circ }={30}^{\circ }$
Now, $n^{{}^{\prime }}=\frac{{360}^{\circ }}{{30}^{\circ }}=12$
For symmetric placement of the object and $n^{{}^{\prime }}$ is even,
Number of images $=n^{{}^{\prime }}-1=12-1=11$