Question

When a ray of light strikes a plane mirror at an angle of ${15}^{\circ }$ with the mirror, what will be the angle through Which the ray gets deviated?

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${75}^{\circ }$
• D. None of these

Answer 1

Answer: (B)

Here, $\theta ={15}^o$

Now, angle of deviation is the angle by which the path of incidence direction is changed.

From figure we can see that direction of incidence is changed by angle

$\alpha +\beta$ and then the ray go along reflected direction.

Hence, angle of deviation$=\delta =\alpha +\beta$

From figure by using equality of vertically opposite angles-

$\alpha =\theta$

Again-

$i={90}^o-\theta$

And, using law of reflection-

$r=i={90}^o-\theta$

And from figure-

$\beta ={90}^o-r={90}^o-({90}^o-\theta )$

$⟹\beta =\theta$

Hence, we get $\delta =\alpha +\beta =\theta +\theta$

$⟹\delta =2\theta$

$⟹\delta =2\times {15}^o={30}^o$

Answer-(B)