Two parallel plane mirrors `M_(1) and M_(2)` have a length of 2 m each and are 10 mm apart. A ray of light is incident on one end of mirror `M_(2)` at an angle of `30^(@)`. The number of reflections light undergoes before reaching the other end is –

Options

A. 346
B. 134
C. 80
D. 173

Explanation

To solve the problem of how many reflections a ray of light undergoes before reaching the other end of the mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- We have two parallel mirrors, M1 and M2, each of length 2 m (2000 mm).
- The distance between the mirrors is 10 mm.

2. **Identify the Angle of Incidence**:
- The ray of light is incident at an angle of \(30^\circ\) to the normal at the end of mirror M2.

3. **Calculate the Vertical Distance (h)**:
- We need to find the vertical distance (h) that the light travels before it reflects off the opposite mirror.
- Using the tangent of the angle of incidence:
\[ \tan(30^\circ) = \frac{h}{10 \text{ mm}} \]
- Since \(\tan(30^\circ) = \frac{1}{\sqrt{3}}\), we can write:
\[ \frac{1}{\sqrt{3}} = \frac{h}{10 \text{ mm}} \implies h = \frac{10 \text{ mm}}{\sqrt{3}} \approx 5.77 \text{ mm} \]

4. **Convert Units**:
- Convert h to meters for consistency:
\[ h = 5.77 \text{ mm} = 5.77 \times 10^{-3} \text{ m} \]

5. **Calculate the Number of Reflections**:
- The total length of the mirror is 2 m (2000 mm).
- The number of reflections can be calculated by dividing the total length of the mirror by the vertical distance (h):
\[ \text{Number of reflections} = \frac{\text{Total Length}}{h} = \frac{2 \text{ m}}{5.77 \times 10^{-3} \text{ m}} \approx 346 \]

### Final Answer:
The number of reflections the light undergoes before reaching the other end is approximately **346**.

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