An incident ray strikes a plane mirror at an angle of `15^@` with the mirror. The angle between the reflected ray and the mirror is

Options

A. `15^@`
B. `30^@`
C. `75^@`
D. none of these

Explanation

To solve the problem, we need to find the angle between the reflected ray and the mirror when an incident ray strikes the mirror at an angle of \(15^\circ\).

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The incident ray strikes the plane mirror at an angle of \(15^\circ\) with respect to the mirror surface.

2. **Identify the Angle of Incidence**:
- The angle of incidence (\(i\)) is measured with respect to the normal (a line perpendicular to the mirror surface).
- Since the incident ray makes an angle of \(15^\circ\) with the mirror, the angle of incidence can be calculated as:
\[ i = 90^\circ - 15^\circ = 75^\circ \]

3. **Apply the Law of Reflection**:
- According to the law of reflection, the angle of incidence is equal to the angle of reflection (\(r\)).
- Therefore, we have:
\[ r = i = 75^\circ \]

4. **Determine the Angle Between the Reflected Ray and the Mirror**:
- The angle between the reflected ray and the mirror can be found by subtracting the angle of reflection from \(90^\circ\):
\[ \text{Angle between reflected ray and mirror} = 90^\circ - r = 90^\circ - 75^\circ = 15^\circ \]

5. **Final Answer**:
- The angle between the reflected ray and the mirror is \(15^\circ\).

### Summary:
The angle between the reflected ray and the mirror is \(15^\circ\).

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