When a mirror is rotated by an angle of θ, the reflected ray will rotate by

1. The question involves the law of reflection concerning a rotating mirror. 2. Let the initial angle of incidence be i. The initial angle of reflection is also i. 3. The angle between the incident ray and the reflected ray is i + i = 2i. 4. Now, the mirror is rotated by an angle θ, keeping the incident ray fixed. 5. When the mirror rotates by θ, the normal to the mirror also rotates by the same angle θ in the same direction. 6. If the mirror rotates such that the angle between the incident ray and the normal increases, the new angle of incidence becomes (i + θ). The new angle of reflection will also be (i + θ). 7. The angle the new reflected ray makes with the original normal is (i + θ) + θ = i + 2θ (relative to the original normal position). The angle the original reflected ray made was i. 8. The change in the angle of the reflected ray (relative to the fixed incident ray direction or a fixed reference) is (i + θ) + θ (angle from new normal) - i = 2θ. Alternatively, consider the angle relative to the incident ray: initial angle is 2i, final angle is 2(i+θ) = 2i + 2θ. The reflected ray rotates by (2i + 2θ) - 2i = 2θ. 9. Thus, if the mirror rotates by an angle θ, the reflected ray rotates by an angle 2θ.