Question

A ray of light incident on the first mirror parallel to the second and is reflected from the second mirror parallel to first mirror. The angle between two mirrors is

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${75}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (B)

Step 1: Given

Let M₁ and M₂ are the mirrors.

The incident ray is parallel to mirror M₂,

The reflected ray is parallel to mirror M₁,

Let the angle between the mirrors is($\angle$BDC) = $\theta$.

Draw a normal for the reflections from the mirrors.

Step 2: Formula used

Angle of incidence= Angle of reflection

Step 3: Finding the angle between the mirrors

Then ∠ M₁BA=$\theta$ and ∠ ECM₂=$\theta$(corresponding angles).

Hence, $\angle$ M₁BA=$\angle$ DBC=$\theta$(linear pair).

Similarly, $\angle$ ECM₂=$\angle$ DCB=$\theta$.

$\angle$DBC +$\angle$DCB +$\angle$BDC =${180}^o$

$\theta$+ $\theta$+ $\theta$ =${180}^o$

3$\theta$ =${180}^o$

$\theta$ =${60}^o$

Hence, the angle between the mirrors is ${60}^o$.