Two plane mirrors are placed perpendicular to each other. A ray strikes one mirror and after reflection falls on the second mirror. The ray after reflection from the second mirror will be

Options

A. perpendicular to the original ray
B. anti parallel to the original ray
C. at `45^@` to the original ray
D. can be at any angle to the original ray

Explanation

To solve the problem of determining the direction of a ray after it reflects off two plane mirrors placed perpendicular to each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors positioned at a right angle (90 degrees) to each other.
- A ray of light strikes one of the mirrors.

**Hint**: Visualize the mirrors as forming an "L" shape, with the angle between them being 90 degrees.

2. **First Reflection**:
- When the ray strikes the first mirror, it reflects off according to the law of reflection, which states that the angle of incidence is equal to the angle of reflection.
- Let’s denote the angle of incidence at the first mirror as θ. Therefore, the angle of reflection will also be θ.

**Hint**: Remember that the angle is measured from the normal (the line perpendicular to the surface of the mirror).

3. **Direction After First Reflection**:
- After reflecting from the first mirror, the ray will travel towards the second mirror. Since the mirrors are perpendicular, the ray will now strike the second mirror at an angle of (90 - θ).

**Hint**: Visualize the path of the ray as it bounces off the first mirror and heads towards the second mirror.

4. **Second Reflection**:
- Upon striking the second mirror, the ray will again reflect according to the law of reflection. The angle of incidence at the second mirror will be (90 - θ), and thus the angle of reflection will also be (90 - θ).

**Hint**: Keep in mind that the angle of incidence and reflection are equal at the second mirror as well.

5. **Direction After Second Reflection**:
- The ray that reflects off the second mirror will now be directed back parallel to the original incoming ray but in the opposite direction.

**Hint**: Consider how the angles add up; the total change in direction after two reflections should lead to a straight line in the opposite direction.

6. **Conclusion**:
- The final direction of the ray after reflecting off both mirrors will be anti-parallel to the original ray. This means that the ray will travel in the exact opposite direction to its initial path.

**Hint**: Think of anti-parallel lines as two lines that run parallel but in opposite directions.

### Final Answer:
The reflected rays will go anti-parallel to the original ray.