The image formed by a concave mirror is real, inverted and magnified, when object is placed

Analyze the question: We need the object position for a concave mirror that gives an image that is real, inverted and magnified (bigger than the object).

Concept: For a concave mirror, the image depends on where the object is placed. Here F is the focus and C is the centre of curvature (C = 2F).

| Object position | Image position | Nature of image | |---|---|---| | Beyond C | Between F and C | Real, inverted, diminished | | At C | At C | Real, inverted, same size | | Between C and F | Beyond C | Real, inverted, magnified | | At F | At infinity | Real, inverted, highly magnified (image not actually formed) | | Between F and the mirror (pole) | Behind the mirror | Virtual, erect, magnified |

Solution with the mirror formula: Take f = 10 cm, so C = 20 cm, and place the object at u = 15 cm, which is between F and C.

1/v = 1/f − 1/u = 1/10 − 1/15 = (3 − 2)/30 = 1/30, so v = 30 cm.

The image is real because v is positive, and it is formed beyond C. Magnification m = v/u = 30/15 = 2, so the image is magnified, and it is inverted.

Checking the other options:

• A (at F): the rays emerge parallel, so no image is formed (it is at infinity).
• B (at C): the image is the same size as the object.
• C (beyond C): the image is diminished.

Answer: The object must be placed between the centre of curvature and the focus, which is option D.

Tip: Remember "Real, inverted, magnified = between C and F". As the object moves from far away toward the mirror, the image grows from small to same size (at C) to large (between C and F). Once the object is inside F, the image becomes virtual.