What is the angle of incidence of a ray if the reflected ray is at an angle of `90^(@)` to the incident ray?

Options

A. 90∘
B. 75∘
C. 45∘
D. None of the above

Explanation

To find the angle of incidence of a ray when the reflected ray is at an angle of 90 degrees to the incident ray, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a ray of light that strikes a mirror (let's assume it's a plane mirror).
- The angle between the incident ray and the reflected ray is given as 90 degrees.

2. **Applying the Laws of Reflection**:
- According to the laws of reflection, the angle of incidence (I) is equal to the angle of reflection (R). This means that if the incident ray makes an angle I with the normal (the line perpendicular to the surface of the mirror), then the reflected ray will also make an angle R with the normal, where I = R.

3. **Setting Up the Angles**:
- If we denote the angle of incidence as I and the angle of reflection as R, we can express the relationship between these angles and the angle between the incident and reflected rays.
- The total angle between the incident ray and the reflected ray is given as 90 degrees. Therefore, we can write:
\[ I + R = 90^\circ \]

4. **Substituting the Angles**:
- Since we know that I = R (from the laws of reflection), we can substitute R with I in the equation:
\[ I + I = 90^\circ \]
- This simplifies to:
\[ 2I = 90^\circ \]

5. **Solving for the Angle of Incidence**:
- To find the angle of incidence, we divide both sides of the equation by 2:
\[ I = \frac{90^\circ}{2} = 45^\circ \]

6. **Conclusion**:
- Therefore, the angle of incidence of the ray is \( 45^\circ \).

### Final Answer:
The angle of incidence is \( 45^\circ \).

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