Two plane mirrors are inclined to each other at an angle of `45^@`. If a ray of light incident on the first mirror is parallel to the second mirror, then it is reflected from the second mirror as

Options

A. Perpendicular to the first mirror
B. Parallel to the first mirror
C. Parallel to the second mirror
D. Perpendicular to the second mirror.

Explanation

To solve the problem, we need to analyze the behavior of light when it interacts with two plane mirrors that are inclined at an angle of 45 degrees.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors (let's call them Mirror 1 and Mirror 2) inclined at an angle of 45 degrees to each other.
- A ray of light is incident on Mirror 1 and is parallel to Mirror 2.

2. **Incident Ray on Mirror 1**:
- Since the ray is parallel to Mirror 2, it means that the angle of incidence on Mirror 1 is equal to the angle between the incident ray and the normal to Mirror 1.

3. **Reflection from Mirror 1**:
- According to the law of reflection, the angle of incidence is equal to the angle of reflection.
- Therefore, the ray will reflect off Mirror 1 at an angle equal to the angle of incidence.

4. **Direction of the Reflected Ray**:
- After reflecting off Mirror 1, the ray will now travel towards Mirror 2.
- Since the mirrors are inclined at 45 degrees, we can visualize the path of the ray.

5. **Incident Ray on Mirror 2**:
- The ray that reflects off Mirror 1 will now strike Mirror 2.
- The angle of incidence on Mirror 2 will also be 45 degrees because of the 45-degree inclination between the mirrors.

6. **Reflection from Mirror 2**:
- Again, applying the law of reflection, the angle of incidence will equal the angle of reflection.
- Since the incident ray on Mirror 2 is at a 45-degree angle, the reflected ray will also be at a 45-degree angle to the normal of Mirror 2.

7. **Final Direction of the Reflected Ray**:
- The reflected ray from Mirror 2 will be perpendicular to Mirror 1 because the angle between the two mirrors is 45 degrees, and the reflected ray makes a 45-degree angle with the normal of Mirror 2.

### Conclusion:
The ray of light is reflected from the second mirror in a direction that is **perpendicular to the second mirror**.