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)
What is the angle of c?

Options

A. `pi`
B. `(pi)/(2)`
C. `(3pi)/(2)`
D. None of these

Answer

To solve the problem, we need to analyze the situation involving two plane mirrors that subtend an angle \( \theta \) between them. A ray of light is incident parallel to one of the mirrors and retraces its path after \( n \) reflections such that \( n\theta = c \), where \( c \) is a constant. Our goal is to find the value of \( c \).

### Step-by-step Solution:

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

2. **Reflection of Light**:
- When the ray hits the second mirror, it reflects off at the same angle it arrived at, which is determined by the angle \( \theta \) between the mirrors.
- The ray will continue to reflect between the mirrors.

3. **Condition for Retracing Path**:
- For the ray to retrace its path, the total angle of deviation after \( n \) reflections must equal \( 360^\circ \) or a multiple of it.
- Each reflection contributes an angle of \( \theta \) to the deviation.

4. **Total Angle of Deviation**:
- After \( n \) reflections, the total deviation is \( n\theta \).
- For the ray to retrace its path, we need \( n\theta = 360^\circ k \) for some integer \( k \).

5. **Finding \( c \)**:
- The problem states that \( n\theta = c \).
- We can set \( c = 360^\circ k \).
- The simplest case is when \( k = 1 \), which gives \( c = 360^\circ \).

6. **Conclusion**:
- Therefore, the constant \( c \) is \( 360^\circ \).

### Final Answer:
The angle \( c \) is \( 360^\circ \).