Two mirrors are inclined at an angle $\theta$ as shown in the figure. Light ray is incident parallel to one of the mirrors. The ray will start retracting its path after third reflection if:

For the light ray to retrace its path after the third reflection, the total angle between the mirrors and the path of the ray must satisfy the condition for periodicity. This can be analyzed using geometry in the triangle formed by the mirrors and the light ray.

Step-by-Step Explanation

1. Geometry of Reflection:

   When the light ray undergoes three reflections, the triangle formed by the light path and the mirrors is ΔABC, where θ is the angle between the mirrors.

2. Sum of Angles in a Triangle:

   In ΔABC, the sum of the internal angles is always 180°:

   90° + 2θ + θ = 180°

3. Simplify the Equation:

   Combine like terms:

   90° + 3θ = 180°

4. Solve for θ:

   Rearrange the equation to isolate θ:

   3θ = 180° - 90°

   3θ = 90°

   θ = 90° / 3

   θ = 30°

Conclusion

The angle between the two mirrors, θ, must be 30° for the light ray to retrace its path after the third reflection. This result demonstrates the geometric conditions required for periodic behavior in reflection setups involving inclined mirrors.