Question

The incident ray and the reflected ray from a mirror is mutually perpendicular to each other. Find the angle of incidence.
A. \[{{0}^{\circ }}\]
B. \[{{90}^{\circ }}\]
C. \[{{30}^{\circ }}\]
D. \[{{45}^{\circ }}\]

Answer 1

Hint: The ray of light which approaches the mirror is known as the incident ray and the ray of light that leaves the mirror is known as the reflected ray. According to the law of reflection, when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.

Complete step by step answer:

Law of reflection:

When light reflects from a plane surface, the angle that the reflected ray makes with the normal at the point of incidence is always equal to the angle the incident ray makes with the same normal.

The incident ray, reflected ray, and normal always lie in the same plane.

Now according to the law of reflection, angle of reflection \[\left( {{\theta }_{r}} \right)\] equals to the angle of incidence \[\left( {{\theta }_{i}} \right)\]. The angles are measured relative to the normal to the surface.

Given that, the incident ray and the reflected ray from a mirror is mutually perpendicular to each other.

So,
 \[{{\theta }_{i}}+{{\theta }_{r}}={{90}^{\circ }}\] --------(1)
Now on applying the law of reflection, we have, \[{{\theta }_{i}}={{\theta }_{r}}\]
On putting \[{{\theta }_{i}}={{\theta }_{r}}\] in equation (1), we get

\[\Rightarrow {{\theta }_{i}}+{{\theta }_{i}}={{90}^{\circ }}\]
\[\Rightarrow 2{{\theta }_{i}}={{90}^{\circ }}\]
\[\Rightarrow {{\theta }_{i}}={{45}^{\circ }}\]

So, the angle of incidence will be \[{{45}^{\circ }}\]

Hence, the correct option is D, i.e., \[{{45}^{\circ }}\]

Note: Students should understand the phenomenon of reflection on a smooth surface. They also need to understand the law of reflection. On applying the law of reflection appropriately, students can find out the required angle easily, by substituting \[{{\theta }_{i}}={{\theta }_{r}}\].