A thin lens forms an image of a real object. The magnification is +2.…

The correct answer is Option (3) → The image is virtual and the lens is convex.

For a lens, a positive magnification means an erect and virtual image. A negative magnification means an inverted and real image.

Option (1) The image is real and the lens is convex. — Incorrect. A real image formed by a lens is inverted, so its \(m\) is negative. Here \(m\) is positive.

Option (2) The image is virtual and the lens is concave. — Incorrect. For a concave lens both \(f\) and \(u\) are negative in \( \frac{1}{v}=\frac{1}{f}+\frac{1}{u} \). This gives \( |v|\lt|u| \), so its image is always smaller than the object. An image 2.5 times larger cannot come from it.

Option (3) The image is virtual and the lens is convex. — Correct. Positive \(m\) gives an erect, virtual image. It is 2.5 times the object, which a convex lens gives when the object is between its focus and the lens.

Option (4) The image is real and the lens is concave. — Incorrect. A concave lens does not form a real image of a real object. A real image would also give a negative \(m\).

NCERT (2026-27):
Refraction by a lens – “When we apply the sign convention, we see that, for erect (and virtual) image formed by a convex or concave lens, m is positive, while for an inverted (and real) image, m is negative.”