Question

What is the angle of incidence of a ray if the reflected ray is at an angle of ${90^\circ}$ to the incident ray?
A) ${30^\circ}$
B) ${45^\circ}$
C) ${180^\circ}$
D) ${90^\circ}$
E) ${60^\circ}$

Answer 1

Hint: The laws of reflection tell us that the incident ray, normal and reflected ray exist on the same plane. And, incident ray and reflected ray are on the opposite sides of the normal.

Complete step by step answer:
Incident ray: The light ray which travels towards the mirror to get reflected is known as Incident Ray.
Normal: A perpendicular line to the mirror drawn at the point of incidence is known as Normal.
Reflected Ray: The light ray which travels away from the mirror after getting reflected is known as Reflected Ray.
Angle of incidence $\left( {\angle i} \right)$: The angle between the incident ray and normal is known as Angle of Incidence.
Angle of reflection $\left( {\angle r} \right)$: The angle between the reflected ray and normal is known as Angle of Reflection.
The third law of reflection states that angle of incidence and angle of reflection are equal. So,
$\angle i = \angle r$
It is given in the question that the reflected ray makes a ${90^\circ}$ angle with the incident ray. So, $\angle i + \angle r = {90^\circ}$
$\Rightarrow 2\angle i = {90^\circ}$
$\Rightarrow \angle i = {45^\circ}$

Hence, the option B is the correct answer.

Note: The laws of reflection are in accordance with Snell’s law. It states that the ratio of sine of angles of incidence and reflection is equal to the ratio of refractive index of one medium to another. That is,
$\dfrac{{{\mu _1}}}{{{\mu _2}}} = \dfrac{{\sin i}}{{\sin r}}$
But, in case of reflection, the medium is the same. So,
$\dfrac{{{\mu _1}}}{{{\mu _2}}} = 1$
$
   \Rightarrow \dfrac{{\sin i}}{{\sin r}} = 1 \\
   \Rightarrow \sin i = \sin r \\
  \therefore i = r $