A real and smaller image of an object will be produced by

The correct answer is Option (1) → a concave mirror, when the object is placed beyond 2F

For a mirror the point "2F" is the centre of curvature C, since \( R = 2f \). A convex mirror always forms a virtual, erect, diminished image, so only a concave mirror can give a real image.

Option (1) a concave mirror, when the object is placed beyond 2F — Correct. For an object beyond C, a concave mirror forms a real, inverted image between F and C, smaller than the object.

Option (2) a convex mirror, when the object is placed between the Pole and the principal focus F — Incorrect. A convex mirror never forms a real image.

Option (3) a concave mirror, when the object is placed between the center of curvature (R) and F — Incorrect. For an object between C and F, the real image is formed beyond C and is enlarged.

Option (4) a convex mirror, when the object is placed beyond 2F — Incorrect. A convex mirror never forms a real image, wherever the object is.