Question

A light ray is incident on a plane mirror, which after getting reflected strikes another plane mirror, as shown in figure. The angle between the two mirrors is ${60}^{\circ }$. Find the angle $\theta$ is shown in figure.

Answer 1

Hint : In this question, we will use angle sum property. A triangle containing three angles and three sides and a pair of neighbouring sides bound each vertex. In a Euclidean period, the sum of triangle angles equals $180$ degrees. It does not matter if the triangle is obtuse, an acute, or a right triangle; the sum of all angles will be $180$ degrees. Thus, the angle sum property says that the sum of the triangle angles is equal to $180$ degrees.

Complete step-by-step solution:
The angle between the two mirrors is ${60}^{\circ }$.
Let $\mathrm{\angle }A=2x$
$\mathrm{\angle }B=2y$
This gives,
$\mathrm{\angle }OAB={90}^{\circ }-x$
$\mathrm{\angle }OBA={90}^{\circ }-y$

In triangle OAB,
Using sum of angle property,
${60}^{\circ }+({90}^{\circ }-x)+({90}^{\circ }-y)={180}^{\circ }$
$⟹{60}^{\circ }-x-y=0$
$⟹x+y={60}^{\circ }$
Now, we will apply sum of angle property,
$\theta +2x+2y={180}^{\circ }$
Put $x+y={60}^{\circ }$ in above formula:
$\theta +2({60}^{\circ })={180}^{\circ }$
$⟹\theta =180–120={60}^{\circ }$
Hence, the angle $\theta$ is ${60}^{\circ }$.

Note: A mirror is a reflective covering that light does not move through but bounces off, producing an image. Mirrors are formed by putting a thin coating of silver nitrate or aluminium following a smooth piece of glass. When we place an object in the face of a mirror, we see the identical object in the mirror.