Question

If the angle of incidence is 50${}^{\circ }$, then calculate the angle through which the incident ray will be deflected :

• A. ${50}^{\circ }$
• B. ${260}^{\circ }$
• C. ${100}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is D ${80}^{\circ }$

Here, $i={50}^o$

Now,angle between incident ray and the reflected ray is the angle between direction of incident and reflected ray.

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

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

Hence, required angle $=\delta =\alpha +\beta$

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 $\delta =\alpha +\beta =\theta +\theta$

$⟹\delta =2\theta =2({90}^o-i)$

$⟹\delta =2({90}^o-{50}^o)$

$⟹\delta ={80}^o$

Answer-(D)