Question

What is the angle of incidence of a ray if the reflected ray is at an angle ${90^0}$ of the incident ray?

Answer 1

Hint: We can draw a diagram fulfilling the conditions given in the question. The angle between incidence and reflected rays is given. By applying the law of reflection, we can get the value of angle of incidence.

Complete step by step answer
 As seen in the diagram, an incident ray falls on a surface of the mirror and the reflected ray r is at ${90^0}$to i. At the point where incident ray i falls on the mirror a normal is drawn. This line divides the angle between the incident and reflected ray equally.
From the law of reflection, we know that the angle of incidence is equal to the angle of reflection. This is also the second law of reflection, written as $\angle i = \angle r$. Let us assume angle of incidence to be x
From the question we know that $\angle i,\angle r$are ${90^0}$apart
Hence, $x + x = {90^0} \Rightarrow x = {45^0}$

So, the value of incidence angle is ${45^0}$

Additional information
We can see objects because of reflection only. The phenomenon of Echo occurs also because of reflection. There are two types of reflection which occurs – Regular reflection and irregular reflection.
Regular reflection- If the process of reflection occurs on a smooth surface, it results in all the reflected rays to be parallel to the incident rays.
Irregular reflection- If rays are reflected from rough or irregular surfaces, the reflected rays do not remain parallel to incident rays.

Note: Bouncing back of light rays on falling to a surface is called reflection. Both regular and irregular reflection follows the law of reflection. Law of reflection is stated as : if a light ray falls on a surface and the reflected ray, incident ray and normal lie in the same plane then the angle of reflection is equal to the angle of incidence.