An object is placed far beyond the centre of curvature of a concave mirror. The object then starts accelerating towards the mirror. Which one of the following is correct?
- A.The image will accelerate towards the centre of curvature.
- B.The image will accelerate towards the focus.
- C.The image will accelerate towards the pole of the mirror.
- D.The image will move with a constant speed towards the focus.
Correct answer
Explanation
The correct answer is A, the image will accelerate towards the centre of curvature. As an object comes in from far away towards C, its real, inverted image moves out from the focus towards C, and the two meet at C.
For a concave mirror, an object at infinity forms its image at the focus F, and an object at the centre of curvature C forms its image at C itself. So while the object travels from far away to C, the image travels from F to C, which is away from the mirror. By the mirror formula 1/v + 1/u = 1/f, the image speed is (v/u)² times the object speed; that ratio grows towards 1 as the object nears C, and the object itself is speeding up, so the image speeds up too.
B is wrong because the image starts near the focus and moves away from it.
C is wrong because the image moves away from the pole, not towards it.
D is wrong on both counts: the speed is not constant and the direction is not towards the focus.
Exam tip: object at infinity, image at F; object at C, image at C; object between C and F, image beyond C.
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