If you combine the formula relating object and image distance with the magnification formula, then solve for object distance, you will see that the distance must be the same as the focal length to get a 1/2 sized image.
Maybe this web site will help.
https://www.quora.com/A-convex-mirror-of-focal-length-f-produces-an-image-of-1-nth-of-the-size-of-the-object-What-is-the-distance-of-the-object-from-the-mirror
Focal length of a convex mirror is 10 cm where should an object be placed in front of a convex mirror so that the image of half the size of the object is formed?
2 answers
Good