To solve the problem of how much the reflected ray is rotated when a plane mirror is rotated, we need to understand the relationship between the angle of incidence, the angle of reflection, and how these angles change when the mirror itself is rotated. ### Step-by-Step Explanation: 1. **Understanding the Basics**: - When a ray of light strikes a plane mirror, it does so at an angle called the angle of incidence (i). According to the law of reflection, the angle of reflection (r) is equal to the angle of incidence. Therefore, if the angle of incidence is 35°, the angle of reflection is also 35°. 2. **Initial Setup**: - Before the mirror is rotated, we have: - Angle of incidence (i) = 35° - Angle of reflection (r) = 35° - The total angle between the incident ray and the reflected ray is 2 * 35° = 70°. 3. **Rotating the Mirror**: - When the mirror is rotated by an angle of 10°, the angle of incidence changes. Specifically, the new angle of incidence becomes: - New angle of incidence (i') = 35° + 10° = 45°. - According to the law of reflection, the new angle of reflection (r') will also be 45°. 4. **Calculating the Change in the Reflected Ray**: - The initial angle between the incident ray and the reflected ray was 70°. - After the mirror is rotated, the new angle between the incident ray and the reflected ray is: - New angle between incident ray and reflected ray = 2 * 45° = 90°. - The change in the angle of the reflected ray due to the rotation of the mirror can be calculated as: - Change in angle = New angle - Initial angle = 90° - 70° = 20°. 5. **Conclusion**: - Therefore, when the mirror is rotated through 10°, the reflected ray is rotated through an angle of 20°. ### Why the Other Options are Incorrect: - **Option A: 70°**: This option suggests that the reflected ray rotates through the same angle as the initial angle of incidence. This is incorrect because the rotation of the mirror affects the angles of incidence and reflection, leading to a smaller change in the reflected ray. - **Option B: 45°**: This option implies that the reflected ray rotates to an angle equal to the new angle of incidence. However, the angle of reflection is also equal to the angle of incidence, and thus the total change is not simply the new angle of incidence. - **Option C: 25°**: This option does not correspond to any logical calculation based on the rotation of the mirror and the resulting angles. The change in the reflected ray is not 25° based on the given rotation of the mirror. ### Summary: - The angle of incidence equals the angle of reflection. - When a mirror is rotated, the angle of incidence increases by the same amount as the rotation. - The total change in the angle of the reflected ray is double the rotation of the mirror. - In this case, a 10° rotation of the mirror results in a 20° rotation of the reflected ray. ### Revision Summary: - The angle of incidence equals the angle of reflection. - A rotation of the mirror affects both angles equally. - The change in the reflected ray is double the angle of mirror rotation. - For a 10° mirror rotation, the reflected ray rotates by 20°.