Question

Two plane mirrors at an angle $\left(x^o\right)$ produces $5$ images of a point. The number of images produced when $x^0$ is decreased to ${(x-30)}^o$ is

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

Answer 1

The correct option is C $11$

when aplan mirror's are inclined at an angle $x^0$ for number of images we use formula -

$\frac{{360}^{\circ }}{x^0}-1=\text{number of images}$

apblying it here $\Rightarrow \frac{{360}^{\circ }}{x^0}-1=5\Rightarrow \frac{{360}^{\circ }}{x^0}=6$

$\therefore \underset{–}{x^{\circ }={00}^{\circ }}$ by doing $x_0-{30}^{\circ }$ ie ${60}^{\circ }-{30}^{\circ }$

$={30}^{\circ }$

no. of images $\Rightarrow \frac{{360}^{\circ }}{{30}^{\circ }}-1=n\therefore n=11$

Hence obtion 'c' is correct.