When two plane mirrors subtend an angle `theta` between them, then a ray of light incident parallel to one of them retraces its path afer n reflections such that `ntheta=c` (where c is constant)
If the angle between mirrors is `60^(@)` . Then light ray retraces its path after n reflections where n is

Options

A. 3
B. 4
C. 2
D. None of these

Answer

To solve the problem, we need to find the value of \( n \) when two plane mirrors subtend an angle of \( \theta = 60^\circ \) between them, and the condition for the ray of light to retrace its path is given by \( n\theta = c \), where \( c \) is a constant.

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- We have two plane mirrors forming an angle \( \theta = 60^\circ \).
- A ray of light is incident parallel to one of the mirrors.

2. **Finding the Condition for Retracing the Path**:
- For the ray to retrace its path after \( n \) reflections, the relationship \( n\theta = c \) must hold true.
- Here, \( c \) is a constant that represents the total angular deviation after \( n \) reflections.

3. **Calculating the Total Angle**:
- Since the angle between the mirrors is \( 60^\circ \), we can express \( c \) in terms of \( n \) and \( \theta \):
\[ c = n \cdot 60^\circ \]

4. **Finding the Value of \( n \)**:
- To find \( n \), we need to determine how many reflections are required for the ray to return to its original path.
- Each reflection changes the direction of the ray by \( 2\theta \) (since it reflects off both mirrors).
- After \( n \) reflections, the total angular deviation will be \( 2n \cdot 60^\circ \).
- For the ray to retrace its path, this total deviation must equal \( 360^\circ \) (a full circle):
\[ 2n \cdot 60^\circ = 360^\circ \]

5. **Solving for \( n \)**:
- Rearranging the equation gives:
\[ 2n \cdot 60 = 360 \]
\[ 120n = 360 \]
\[ n = \frac{360}{120} = 3 \]

6. **Conclusion**:
- The value of \( n \), which is the number of reflections required for the ray to retrace its path, is \( 3 \).

### Final Answer:
The ray retraces its path after \( n = 3 \) reflections.