At which position should an object be placed in front of a concave mirror in order to obtain an image which is of the same size as the object?

Step 1: Analyze the question We need the object position that gives an image the same size as the object (magnification, m = 1) in a concave mirror.

Step 2: Concept Magnification: m = image distance / object distance = v/u (magnitude). Mirror formula: 1/f = 1/u + 1/v

For the image to be the same size, |v| = |u|.

Step 3: Solution Set v = u in the mirror formula:

1/f = 1/u + 1/u = 2/u

u = 2f

Since the radius of curvature is r = 2f, the object must be placed at u = r, which is the centre of curvature (C).

Check against the other positions:

• At F (B): the image forms at infinity, so it is not the same size.
• Between P and F (C): the image is virtual, upright and magnified.
• Between C and F (D): the image is real, inverted and magnified, formed beyond C.
• Beyond C: the image is diminished.

At C, the image is real, inverted, the same size as the object, and also formed at C.

Answer: A. at the centre of curvature

Tip: Remember "2F rule": at 2F (the centre of curvature), the object and image are the same size, the same distance away, and the image is inverted. Object at C → image at C, m = 1.