A convex lens P has a focal length of 40 cm. Another convex lens Q has a power of +2 D. Which of the following is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → P has the larger power and bends a parallel beam more than Q.
The power of a lens is \(P=1/f\), with \(f\) in metres. To compare the two lenses, find the power of P and the focal length of Q.
\( \begin{aligned} P_P &= \frac{1}{f_P} \\ &= \frac{1}{0.40\ \mathrm{m}} \\ &= +2.5\ \mathrm{D} \end{aligned} \)
\( \begin{aligned} f_Q &= \frac{1}{P_Q} \\ &= \frac{1}{2\ \mathrm{D}} \\ &= 0.5\ \mathrm{m} = 50\ \mathrm{cm} \end{aligned} \)
Option (1) Q has the larger power and bends a parallel beam more than P. — Incorrect. Q has 2 D and P has 2.5 D. To find the power of P, its focal length must be taken in metres.
Option (2) P has the larger power but bends a parallel beam less than Q. — Incorrect. A lens with more power bends a parallel beam more. P has the larger power, so it cannot bend the beam less.
Option (3) Q has the shorter focal length and bends a parallel beam more than P. — Incorrect. The focal length of Q is 0.5 m, that is 50 cm. This is longer than the 40 cm of P, so Q bends the beam less.
Option (4) P has the larger power and bends a parallel beam more than Q. — Correct. P has 2.5 D against 2 D for Q. Its shorter focal length makes it converge a parallel beam more strongly.
NCERT (2026-27):
Power of a lens – “Power of a lens is a measure of the convergence or divergence, which a lens introduces in the light falling on it. Clearly, a lens of shorter focal length bends the incident light more, while converging it in case of a convex lens and diverging it in case of a concave lens. …”
Summary – “… The power of a lens P = 1/f.”
Summary – “The SI unit for power of a lens is dioptre (D): 1 D = 1 m–1.”