Question

The focal length of a convex lens is f. An object is
placed at a distance x from its first focal point. Find
the ratio of the distance of the real image to that
of the object from the pole.​

Answer 1

The image will be a virtual image (behind the mirror) between the pole and the focus.

The position of the image can be calculated from the well-known mirror formula:

1/f = 1/do + 1/di where “do” is the distance of the object from the pole and “di” is the distance of the image from the pole.

You need to be careful with the signs (+ or -) for the distances. Unfortunately there is more than one “sign convention”. What I’ve used here is the convention that virtual image distances are negative and the focal length of a convex mirror is also negative.

I get the answer as: image distance = f/2, behind the mirror.

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