Question

A light ray is incident on a flat surface, making an angle of ${20}^{\circ }$ with the surface. Find (i) the angle between the incident ray and the reflected ray (ii) the angle between the reflected ray and the surface?

• A. ${70}^{\circ },{20}^{\circ }$
• B. ${70}^{\circ },{70}^{\circ }$
• C. ${140}^{\circ },{20}^{\circ }$
• D. ${20}^{\circ },{70}^{\circ }$

Answer 1

The correct option is C ${140}^{\circ },{20}^{\circ }$

Let the angle of incidence and angle of reflection be $i$ and $r$ respectively.
Since the angle between the surface and normal is ${90}^{\circ }$
$\therefore \angle i+{20}^{\circ }={90}^{\circ }$
$\Rightarrow \angle i={90}^{\circ }-{20}^{\circ }={70}^{\circ }$
We know that the law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.
$\Rightarrow \angle i=\angle r={70}^{\circ }$
Hence, the angle between the incident ray and the reflected ray is $\angle i+\angle r={70}^{\circ }+{70}^{\circ }={140}^{\circ }$
The angle between the reflected ray and the surface is:
${90}^{\circ }-\angle r={90}^{\circ }-{70}^{\circ }={20}^{\circ }$