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

Last updated date: 13th Jun 2024
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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.

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}\$