A convex lens forms a real image of a small object. The object stands upright on the principal axis, beyond the focus. Using the Cartesian sign convention, how many of the following quantities are negative?
Object distance \(u\), image distance \(v\), focal length \(f\), power \(P\), magnification \(m\), height \(h\) of the object, height \(h^{\prime}\) of the image
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Three
In the Cartesian sign convention, distances measured in the direction of the incident light are positive. Distances measured against it are negative. Heights above the principal axis are positive and heights below it are negative.
The quantities that are negative:
Object distance \(u\) — the object is on the side from which the light comes, so \(u\) is measured against the light.
Magnification \(m\) — a real image formed by a lens is inverted, so \(m\) is negative.
Height \(h^{\prime}\) of the image — the inverted image lies below the principal axis.
The quantities that are not negative:
Image distance \(v\) — the real image forms on the other side of the lens, along the light.
Focal length \(f\) — positive for a converging lens.
Power \(P\) — positive for a converging lens.
Height \(h\) of the object — the object stands upright, above the axis.
Number of negative quantities = 3
NCERT (2026-27):
Summary – “3. Cartesian sign convention: Distances measured in the same direction as the incident light are positive; those measured in the opposite direction are negative. …”
Summary – “… The heights measured upwards above x-axis and normal to the principal axis of the mirror/ lens are taken as positive. The heights measured downwards are taken as negative.”
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.”
Power of a lens – “… Power of a lens is positive for a converging lens and negative for a diverging lens. …”
Summary – “… f is positive for a converging lens; f is negative for a diverging lens. …”