A source of light lies on the angle bisector of two plane mirrors inclined at angle `theta`. The value of `theta`, so that the light reflected from one mirror does not reach the other mirror will be.

Options

A. `thetage120^@`
B. `thetage90^@`
C. `thetale120^@`
D. None of the above

Answer

To solve the problem, we need to determine the angle \( \theta \) between two plane mirrors such that the light reflected from one mirror does not reach the other mirror.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors inclined at an angle \( \theta \).
- A light source is located on the angle bisector of the two mirrors.

2. **Image Formation by Mirrors**:
- When light reflects off a mirror, it creates an image. The number of images formed by two mirrors inclined at an angle \( \theta \) can be calculated using the formula:
\[ n = \frac{360^\circ}{\theta} - 1 \]
- Here, \( n \) is the number of images formed.

3. **Condition for Light Reflection**:
- We want the light reflected from one mirror to not reach the other mirror. This means we want the number of images \( n \) to be less than or equal to 2:
\[ n \leq 2 \]

4. **Setting Up the Inequality**:
- Substituting the expression for \( n \) into the inequality:
\[ \frac{360^\circ}{\theta} - 1 \leq 2 \]

5. **Solving the Inequality**:
- Rearranging the inequality gives:
\[ \frac{360^\circ}{\theta} \leq 3 \]
- Multiplying both sides by \( \theta \) (assuming \( \theta > 0 \)):
\[ 360^\circ \leq 3\theta \]
- Dividing both sides by 3:
\[ \theta \geq \frac{360^\circ}{3} \]
- Simplifying:
\[ \theta \geq 120^\circ \]

6. **Conclusion**:
- Therefore, the value of \( \theta \) so that the light reflected from one mirror does not reach the other mirror must be:
\[ \theta \geq 120^\circ \]

### Final Answer:
The angle \( \theta \) should be greater than or equal to \( 120^\circ \).