What is the angle of incidence of a ray if the reflected ray is at an angle of 90° to the incident ray?

1. Break Down the Problem

We need to find the angle of incidence of an incident ray when the reflected ray is at an angle of 90° to the incident ray.

2. Relevant Concepts

According to the law of reflection:

• The angle of incidence ($i$) is equal to the angle of reflection ($r$).
• The sum of the angle of incidence and the angle of reflection determines the angle between the incident and reflected rays.

3. Analysis and Detail

Let:

• $i$ = angle of incidence
• $r$ = angle of reflection

According to the law of reflection: $i = r$

It's given that the angle between the incident ray and the reflected ray is 90°. Therefore, we can express this as: $i + r = 90^\circ$

Substituting $r$ with $i$: $i + i = 90^\circ$ $2i = 90^\circ$

4. Verify and Summarize

Now, solving for $i$: $i = \frac{90^\circ}{2} = 45^\circ$

Final Answer

The angle of incidence of the ray is $45^\circ$.