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

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Given:
The reflected ray is at an angle of $90^{\circ}$ to the incident ray.

To do:
We have to find the angle of incidence of the ray.

Solution:
To find the angle of the incidence of the ray, let us know a little about what the law of reflection states:
Law of reflection:
"The angle of incidence is equal to the angle of reflection."

$\angle i=\angle r$
Here $\angle i\rightarrow$the angle of incidence
$\angle r\rightarrow$ The angle of reflection
By using the law of reflection let us find the angle of incidence of the ray:

Here, the angle between the incident ray and reflected ray is $90^{\circ}$.

$\angle i+\angle r=90^{\circ}$

Since, $\angle i=\angle r$

We can write, $\angle i+\angle i=90^{\circ}$

Or $2\angle i=90^{\circ}$

Or $\angle i=45^{\circ}$

Therefore, the angle of incidence of the ray is $45^{\circ}$.
Updated on 10-Oct-2022 13:25:19