if the incident ray is rotated clock wise by 30 degrees, and the mirror is rotated by 15 degrees in the anti - clock wise direction, then by what angle does the reflected ray rotate?

The angle of incidence is equal to the angle of reflection in a mirror. This is known as the law of reflection.

1. If the incident ray is rotated clockwise by 30 degrees, the angle of incidence decreases by 30 degrees.

2. If the mirror is rotated 15 degrees in the anti-clockwise direction, the angle of incidence increases by 15 degrees because the incident ray and the mirror move in opposite directions.

3. Therefore, the total change in the angle of incidence is -30 degrees + 15 degrees = -15 degrees.

4. According to the law of reflection, the angle of reflection changes by the same amount as the angle of incidence.

5. Therefore, the reflected ray rotates by -15 degrees.

6. However, the direction of rotation of the reflected ray is opposite to that of the incident ray.

7. So, if a negative rotation is clockwise, then a negative rotation for the reflected ray is anti-clockwise.

8. Therefore, the reflected ray rotates 15 degrees anti-clockwise.