Question

A real object is placed at a distance f from the pole of a convex mirror if the focal length of the mirror is f the distance of the image from the pole of the mirror is

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.