Two plane mirror are inclined to each other at `90^(@)`. A ray of light is incident on one mirror. The ray will undergo a total deviation of

Options

A. `180^(@)`
B. `90^(@)`
C. `45^(@)`
D. Cannot be found because angle of incidence is not given

Explanation

To solve the problem of finding the total deviation of a ray of light when it is incident on one of two plane mirrors inclined at an angle of 90 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have two plane mirrors (let's call them Mirror 1 and Mirror 2) that are inclined at an angle of 90 degrees to each other.
- A ray of light is incident on Mirror 1.

2. **Incident Ray and Reflection**:
- Let the angle of incidence on Mirror 1 be \( I \).
- According to the law of reflection, the angle of reflection will also be \( I \).
- Thus, the ray reflects off Mirror 1 at an angle \( I \) to the normal.

3. **Determine the Path of the Ray**:
- After reflecting off Mirror 1, the ray will travel towards Mirror 2.
- The angle between the reflected ray from Mirror 1 and the normal to Mirror 2 will be \( 90 - I \) because the mirrors are at 90 degrees to each other.

4. **Reflection from Mirror 2**:
- The ray now acts as the incident ray for Mirror 2.
- By the law of reflection, it will reflect off Mirror 2 at an angle \( 90 - I \) to the normal, which means it will reflect at an angle \( 90 - (90 - I) = I \) to the normal of Mirror 2.

5. **Final Direction of the Ray**:
- After reflecting off Mirror 2, the ray will be parallel to the original incident ray on Mirror 1 but in the opposite direction.

6. **Calculate Total Deviation**:
- The total deviation is calculated as the difference between the original direction of the incident ray and the final direction of the reflected ray.
- Since the final reflected ray is parallel to the incident ray but in the opposite direction, the total deviation is \( 180^\circ \).

### Conclusion:
The total deviation of the ray of light after reflecting off both mirrors is \( 180^\circ \).