A ray of light incident on the first mirror and parallel to the second mirror in reflected from the second mirror parallel to the first mirror .The angle between the two mirrors is

Options

A. `30^@`
B. `60^@`
C. `70^@`
D. `90^@`

Answer

To solve the problem of finding the angle between two mirrors given the behavior of a ray of light, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup:**
- We have two mirrors, Mirror 1 and Mirror 2, placed at an angle θ to each other.
- A ray of light is incident on Mirror 1 and is parallel to Mirror 2.

2. **Identifying the Angles:**
- When the ray of light hits Mirror 1, it makes an angle of incidence with respect to the normal (perpendicular) to the mirror.
- Since the ray is parallel to Mirror 2, the angle of incidence (i) at Mirror 1 is equal to θ.

3. **Applying the Law of Reflection:**
- According to the law of reflection, the angle of incidence is equal to the angle of reflection.
- Therefore, the angle of reflection (r) from Mirror 1 is also θ.

4. **Analyzing the Reflection from Mirror 2:**
- The reflected ray from Mirror 1 then strikes Mirror 2.
- The angle of incidence at Mirror 2 will be (90° - θ) because the angle between the normal to Mirror 2 and the incoming ray is (90° - θ).
- By the law of reflection, the angle of reflection at Mirror 2 will also be (90° - θ).

5. **Determining the Final Direction of the Ray:**
- The reflected ray from Mirror 2 is parallel to Mirror 1.
- This means that the angle between the reflected ray and the normal to Mirror 2 is also θ.

6. **Setting Up the Equation:**
- We can now analyze the triangle formed by the angles at the point of intersection of the two mirrors.
- The angles in this triangle are θ (from Mirror 1), θ (from Mirror 2), and the angle between the two mirrors, which is θ.
- The sum of the angles in a triangle is 180°.
- Therefore, we can write the equation:
\[ θ + θ + θ = 180° \]
\[ 3θ = 180° \]
\[ θ = \frac{180°}{3} = 60° \]

7. **Conclusion:**
- The angle between the two mirrors is θ = 60°.

### Final Answer:
The angle between the two mirrors is **60 degrees**.