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

• A) 0°
• B) θ / 2
• C) θ
• D) 2θ

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According to the laws of reflection, when an incident ray is kept fixed and a plane mirror is rotated by an angle θ, the reflected ray rotates by an angle of 2θ.

Proof:

• Let the initial angle of incidence be i. The angle of reflection is also i. The angle between the incident and reflected ray is 2i.
• If the mirror is rotated by an angle θ, its normal also rotates by θ.
• The new angle of incidence becomes (i + θ).
• The new angle of reflection is also (i + θ). The new total angle between the incident and reflected ray is 2(i + θ) = 2i + 2θ.
• Since the incident ray is fixed, the reflected ray has rotated by the difference: (2i + 2θ) - 2i = 2θ.