Which of the following statements about the power of a lens is NOT co…

The correct answer is Option (4) → A lens of power +2.5 D is a convex lens of focal length +25 cm.

The power of a lens is \( P=1/f \), with \( f \) in metres. Its sign follows the sign of the focal length in the Cartesian sign convention.

For the lenses of power −4.0 D and +2.5 D the focal lengths are:

    \( \begin{aligned} f_1 &= \frac{1}{-4.0\,\mathrm{D}} \\ &= -0.25\,\mathrm{m} \\ &= -25\,\mathrm{cm} \end{aligned} \)

    \( \begin{aligned} f_2 &= \frac{1}{+2.5\,\mathrm{D}} \\ &= +0.40\,\mathrm{m} \\ &= +40\,\mathrm{cm} \end{aligned} \)

Option (1) The SI unit of the power of a lens is the dioptre, where \( 1\,\mathrm{D}=1\,\mathrm{m^{-1}} \). — Correct statement. A lens of focal length 1 m has a power of one dioptre, so the dioptre is the inverse metre.

Option (2) The power of a converging lens is positive and that of a diverging lens is negative. — Correct statement. A converging lens has a positive focal length and a diverging lens a negative one, and \( P \) takes the same sign as \( f \).

Option (3) A lens of power −4.0 D is a concave lens of focal length −25 cm. — Correct statement. Its focal length is \( -25\,\mathrm{cm} \), and the negative sign marks a diverging, that is concave, lens.

Option (4) A lens of power +2.5 D is a convex lens of focal length +25 cm. — Not correct. The lens is convex because its power is positive, but its focal length is \( +40\,\mathrm{cm} \). A focal length of +25 cm belongs to a lens of power +4.0 D.

NCERT (2026-27):
Power of a Lens – “The SI unit for power of a lens is dioptre (D): 1D = 1m^–1. The power of a lens of focal length of 1 metre is one dioptre. Power of a lens is positive for a converging lens and negative for a diverging lens. Thus, when an optician prescribes a corrective lens of power + 2.5 D, the required lens is a convex lens of focal length + 40 cm. A lens of power of – 4.0 D means a concave lens of focal length – 25 cm.”