Question

Two mirrors are inclined at an angle $\theta$. For an object placed along the angular bisector of the two mirrors, $11$ images are noticed. Find the angle between the mirrors :

• A. ${30}^{\circ }$
• B. ${32.8}^{\circ }$
• C. ${16.4}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

Number of images for the system of mirrors, $n=11$ (odd number).

If the object is placed on the angular bisector of the two plane mirrors inclined to each other at an angle $\theta$, then number of images $n=(\frac{360}{\theta }-1)$

Substituting the given data we get,

$(\frac{360}{\theta }-1)=11$
$\Rightarrow \frac{360}{\theta }=12\Rightarrow \theta ={30}^{\circ }$

Hence, option (a) is the correct answer.