A ray of light is incident at an angle of `60^@` on a horizontal plane mirror. Through what angle should the mirror br tilted to make the reflected ray horizontal ?

Explanation

To solve the problem, we need to understand the behavior of light when it reflects off a mirror. The angle of incidence is equal to the angle of reflection, according to the law of reflection.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The angle of incidence (i) = 60°.
- The mirror is initially horizontal.

2. **Understanding the Reflection**:
- When light strikes a mirror, the angle of incidence is measured from the normal (a line perpendicular to the surface of the mirror).
- The angle of reflection (r) will also be 60° since the angle of incidence equals the angle of reflection.

3. **Determine the Current Position of the Reflected Ray**:
- Since the mirror is horizontal, the normal to the mirror is vertical. Thus, the reflected ray will make an angle of 60° with the normal, which means it will be at an angle of (90° - 60°) = 30° with the horizontal.

4. **Goal**:
- We want the reflected ray to be horizontal, which means it should make an angle of 0° with the horizontal.

5. **Finding the Required Tilt of the Mirror**:
- To make the reflected ray horizontal, we need to change the angle of incidence. If we tilt the mirror by an angle θ, the new angle of incidence will be (60° + θ).
- For the reflected ray to be horizontal, the angle of reflection must also be 90° (since it will be horizontal). Therefore, we set up the equation:
\[ 60° + θ = 90° \]

6. **Solve for θ**:
- Rearranging the equation gives:
\[ θ = 90° - 60° = 30° \]

7. **Conclusion**:
- The mirror should be tilted by 30° to make the reflected ray horizontal.

### Final Answer:
The mirror should be tilted by 30°.