Two plane mirrors are making an angle of `60^(@)` to each other. A light ray falls on one of the mirrors. The light ray is incident parallel to angular bisector of mirrors. How many reflection does the light ray undergo?

Answer

To solve the problem of how many reflections a light ray undergoes when it strikes two plane mirrors inclined at an angle of \(60^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
We have two plane mirrors, \(M_1\) and \(M_2\), making an angle of \(60^\circ\) with each other. A light ray is incident on one of the mirrors, and it is stated that the ray is incident parallel to the angular bisector of the angle formed by the two mirrors.

**Hint**: Visualize the mirrors and the angle they form. Draw the mirrors and the angular bisector to clarify the situation.

2. **Identifying the Angle of Incidence**:
Since the light ray is incident parallel to the angular bisector, it makes an angle of \(30^\circ\) with each mirror. This is because the angular bisector divides the \(60^\circ\) angle into two equal \(30^\circ\) angles.

**Hint**: Remember that the angular bisector divides the angle between the two mirrors into two equal parts.

3. **First Reflection on Mirror \(M_1\)**:
The light ray strikes mirror \(M_1\) at an angle of incidence of \(30^\circ\). According to the law of reflection, the angle of reflection will also be \(30^\circ\).

**Hint**: Use the law of reflection which states that the angle of incidence is equal to the angle of reflection.

4. **Second Reflection on Mirror \(M_2\)**:
After reflecting off \(M_1\), the ray will now act as the incident ray for mirror \(M_2\). The angle of incidence at \(M_2\) will also be \(30^\circ\) (since the ray reflects at the same angle it strikes). Thus, it reflects off \(M_2\) at an angle of \(30^\circ\).

**Hint**: Keep track of the angles as the ray reflects off each mirror.

5. **Third Reflection on Mirror \(M_1\)**:
The ray then reflects off \(M_2\) and returns to mirror \(M_1\). The angle of incidence at \(M_1\) will again be \(30^\circ\), leading to a reflection at \(30^\circ\).

**Hint**: Each time the ray strikes a mirror, check the angle of incidence.

6. **Final Path**:
After reflecting off \(M_1\) for the third time, the ray will retrace its path back to the original direction it came from. This indicates that the ray has undergone a total of three reflections.

**Hint**: Visualize or sketch the path of the light ray to confirm the number of reflections.

### Conclusion:
The light ray undergoes a total of **three reflections** before it retraces its path.