Correct Option (d):
When a plane mirror is rotated by an angle θ, its normal also rotates by the same angle θ. If the incident ray remains fixed, the angle of incidence with respect to the new normal changes. According to the law of reflection, the angle of reflection is equal to the angle of incidence. Consequently, the reflected ray rotates by an angle that is twice the angle of rotation of the mirror, i.e., 2θ. This phenomenon is a direct consequence of the law of reflection and the geometry of reflection.
Incorrect Options:
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Option (a) 0º: If the mirror rotates, the orientation of its normal changes. Given a fixed incident ray, the angle of incidence changes, leading to a change in the direction of the reflected ray. Therefore, the reflected ray does not remain stationary.
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Option (b) θ/2: This value is less than the actual rotation of the reflected ray. The change in the reflected ray's direction is twice the mirror's rotation, not half.
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Option (c) θ: The reflected ray rotates by twice the angle of the mirror's rotation, not by an equal angle. This option incorrectly equates the rotation of the reflected ray with that of the mirror.