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

__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 $45^{\circ}$.

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