A plane mirrorr makes an angle of `30^(@)` with horizontal. If a vertical ray strikes mirrorr, find the angle between mirrorr and reflected ray

Options

A. `30^@`
B. `45^@`
C. `60^@`
D. `90^@`

Explanation

To solve the problem step by step, we will analyze the situation involving the plane mirror and the incident ray.

### Step-by-Step Solution:

1. **Identify the Orientation of the Mirror**:
The plane mirror is inclined at an angle of \(30^\circ\) with the horizontal.

2. **Determine the Angle of Incidence**:
The vertical ray striking the mirror makes an angle of \(90^\circ\) with the horizontal. Since the mirror is inclined at \(30^\circ\), we can find the angle between the incident ray and the normal to the mirror.
- The angle between the vertical ray and the normal (which is perpendicular to the mirror surface) can be calculated as:
\[ \text{Angle with normal} = 90^\circ - 30^\circ = 60^\circ \]
- Therefore, the angle of incidence \(i\) is \(30^\circ\).

3. **Apply the Law of Reflection**:
According to the law of reflection, the angle of incidence is equal to the angle of reflection:
\[ i = r \]
Thus, the angle of reflection \(r\) is also \(30^\circ\).

4. **Find the Angle Between the Reflected Ray and the Mirror**:
We need to find the angle \(\theta\) between the reflected ray and the mirror surface.
- The angle between the reflected ray and the normal is \(30^\circ\).
- Therefore, the angle between the reflected ray and the mirror surface can be calculated as:
\[ \theta = 90^\circ - r = 90^\circ - 30^\circ = 60^\circ \]

5. **Conclusion**:
The angle between the mirror and the reflected ray is \(60^\circ\).

### Final Answer:
The angle between the mirror and the reflected ray is \(60^\circ\).

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