Rays of light strike a horizontal plane mirror at an angle of `45^(@)`.: At what angle should a second mirror be placed so that the final reflected ray emerged in the horizontal direction?

Answer

To solve the problem, we need to determine the angle at which the second mirror should be placed so that the final reflected ray emerges in the horizontal direction after reflecting off both mirrors.

### Step-by-Step Solution:

1. **Understanding the First Reflection**:
- A ray of light strikes the first horizontal mirror at an angle of incidence of \(45^\circ\).
- According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the ray will reflect off the first mirror at an angle of \(45^\circ\) as well.

2. **Direction of the Reflected Ray**:
- After reflecting from the first mirror, the ray will be at an angle of \(45^\circ\) to the normal of the first mirror. Since the mirror is horizontal, this means the reflected ray will be directed upwards at a \(45^\circ\) angle to the horizontal.

3. **Positioning the Second Mirror**:
- We need to place a second mirror such that the ray, after reflecting off this second mirror, emerges horizontally.
- Let's denote the angle between the second mirror and the horizontal as \(\theta\).

4. **Analyzing the Angles**:
- The angle of incidence on the second mirror will be equal to the angle of the incoming ray with respect to the normal of the second mirror.
- The angle between the incoming ray (which is at \(45^\circ\) to the horizontal) and the normal to the second mirror can be expressed as \(90^\circ - \theta\).

5. **Setting Up the Equation**:
- For the ray to emerge horizontally after reflecting off the second mirror, the angle of reflection must be \(0^\circ\) (horizontal).
- Thus, the angle of incidence on the second mirror can be expressed as:
\[ 90^\circ - \theta + \theta = 90^\circ \]
- The total angle from the incoming ray to the horizontal after reflection must equal \(90^\circ\).

6. **Calculating the Required Angle**:
- From the previous steps, we can set up the equation:
\[ 45^\circ + \theta = 90^\circ \]
- Solving for \(\theta\):
\[ \theta = 90^\circ - 45^\circ = 45^\circ \]

7. **Conclusion**:
- Therefore, the second mirror should be placed at an angle of \(45^\circ\) to the horizontal.

### Final Answer:
The second mirror should be placed at an angle of \(45^\circ\) to the horizontal.