Which of the following correctly depicts reflec tions in case of plane mirrors inclined at `40^@`?

Options

A.
B.
C.
D.

Answer

To solve the problem of determining which depiction correctly shows reflections in the case of plane mirrors inclined at 40°, we will analyze each option step by step based on the principles of reflection.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors inclined at an angle of 40° to each other.
- According to the law of reflection, the angle of incidence (i) is equal to the angle of reflection (r).

2. **Analyzing Each Option**:
- **Option 1**:
- Given angle of incidence = 50°.
- Therefore, angle of reflection = 50°.
- The angle between the mirrors is 40°.
- The total angle in the triangle formed is:
- 90° (right angle) + 40° (angle between mirrors) + 50° (angle of incidence) = 180°.
- This option is correct since the sum of the angles is 180°.

- **Option 2**:
- Given angle of incidence = 30°.
- Therefore, angle of reflection = 30°.
- The angle between the mirrors is 40°.
- The total angle in the triangle formed is:
- 90° (right angle) + 40° (angle between mirrors) + 30° (angle of incidence) = 160°.
- This option is incorrect since the sum of the angles is not 180°.

- **Option 3**:
- Given angle of incidence = 50°.
- Therefore, angle of reflection = 50°.
- The angle between the mirrors is 40°.
- The total angle in the triangle formed is:
- 90° (right angle) + 40° (angle between mirrors) + 50° (angle of incidence) = 180°.
- However, the interior angles do not sum correctly, leading to a contradiction. Thus, this option is incorrect.

- **Option 4**:
- Given angle of incidence = 45°.
- Therefore, angle of reflection = 45°.
- The angle between the mirrors is 40°.
- The total angle in the triangle formed is:
- 90° (right angle) + 40° (angle between mirrors) + 45° (angle of incidence) = 175°.
- This option is incorrect since the sum of the angles is not 180°.

3. **Conclusion**:
- After analyzing all options, only **Option 1** correctly depicts the reflections with the sum of the interior angles equaling 180°.

### Final Answer:
**The correct depiction of reflections in case of plane mirrors inclined at 40° is Option 1.**