Two plans mirrors are inclined to each other at some angle .A ray of light incident at `30^(@)`on one,after reflection form the other retraces its path .The angles between the mirrors is:

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@`
D. `90^(@)`

Answer

To solve the problem, we need to determine the angle between two plane mirrors given that a ray of light incident at \(30^\circ\) on one mirror retraces its path after reflecting off the other mirror.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors inclined at an angle \(\theta\).
- A ray of light strikes the first mirror at an angle of incidence \(i = 30^\circ\).

2. **Reflection from the First Mirror**:
- According to the law of reflection, the angle of reflection \(r\) is equal to the angle of incidence \(i\). Thus, \(r = 30^\circ\).
- The ray reflects off the first mirror and travels towards the second mirror.

3. **Incident Angle on the Second Mirror**:
- For the ray to retrace its path after reflecting off the second mirror, it must strike the second mirror at an angle of incidence such that it reflects back along the same path.
- This means that the angle of incidence on the second mirror must be \(90^\circ\).

4. **Analyzing the Geometry**:
- The angle between the two mirrors is \(\theta\).
- The angle of incidence on the second mirror can be expressed as the sum of the angle of reflection from the first mirror and the angle between the mirrors:
\[ \text{Angle of incidence on second mirror} = \theta + 30^\circ \]
- For the ray to retrace its path, this angle must equal \(90^\circ\):
\[ \theta + 30^\circ = 90^\circ \]

5. **Solving for \(\theta\)**:
- Rearranging the equation gives:
\[ \theta = 90^\circ - 30^\circ = 60^\circ \]

6. **Conclusion**:
- Therefore, the angle between the two mirrors is \(\theta = 60^\circ\).

### Final Answer:
The angle between the mirrors is \(60^\circ\).