A point object approaches a plane mirror with a speed of 10 m s⁻¹, while the image recedes away from the mirror with a speed of 6 m s⁻¹ (as seen by stationary observer). The direction and magnitude of the velocity of mirror is :-
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Question

A point object approaches a plane mirror with a speed of 10 m s⁻¹, while the image recedes away from the mirror with a speed of 6 m s⁻¹ (as seen by stationary observer). The direction and magnitude of the velocity of mirror is :-

Options

G1 Physics · Accepted Answer

Derived solution: Step 1: Use the law of reflection i = r and plane-mirror symmetry. The image is as far behind the mirror as the object is in front; rotation of a mirror by φ rotates the reflected ray by 2φ. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is away from the object, 8 m s⁻¹. Therefore the correct option is C.