A ray is reflected in turn by three plain mirrors mutually at right angles to each other. The angle between the incident and the reflected rays is

Options

A. `90^@`
B. `60^@`
C. `180^@`
D. None of these

Answer

To solve the problem of finding the angle between the incident and the reflected rays after reflection from three mutually perpendicular plane mirrors, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have three plane mirrors arranged at right angles to each other. This means that each mirror is perpendicular to the other two. Visualize this as three walls of a room, where light can reflect off each wall.

2. **Incident Ray**:
- Consider an incident ray approaching the first mirror. When the ray strikes the first mirror, it will reflect according to the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

3. **First Reflection**:
- After the incident ray hits the first mirror, it reflects off at an angle equal to the angle of incidence. Let’s denote the angle of incidence as θ. Thus, the angle of reflection will also be θ.

4. **Second Reflection**:
- The reflected ray from the first mirror now hits the second mirror. Again, applying the law of reflection, the angle of incidence at the second mirror will also be θ, resulting in a reflection at the same angle θ.

5. **Third Reflection**:
- The ray then travels to the third mirror. It will again reflect off this mirror following the same law of reflection. The angle of incidence at the third mirror will also be θ, resulting in a reflection at angle θ.

6. **Final Position of the Ray**:
- After reflecting off all three mirrors, we can analyze the direction of the final reflected ray. Since the mirrors are arranged at right angles, the final reflected ray will be in the opposite direction to the original incident ray.

7. **Calculating the Angle**:
- The angle between the original incident ray and the final reflected ray can be determined. Since the final ray is in the opposite direction to the incident ray, the angle between them is 180 degrees.

### Conclusion:
The angle between the incident ray and the reflected ray after reflecting off three mutually perpendicular mirrors is **180 degrees**.