Which of the following statement(s) is/are correct?
(A) The power of a lens is the ability of the lens to converge or diverge the incident rays.
(B) S.I unit of the power of a lens is dioptre while focal length is in centimetres
(C) For a lens of larger focal length, power is smaller
(D) In any combination of lenses, the power of combination is not algebraic addition of power of combined lenses
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (C) only
The power of a lens is \( P = 1/f \), with \( f \) in metres, and it is measured in dioptres.
(A) The power of a lens is the ability of the lens to converge or diverge the incident rays. — Correct. This is the definition of the power of a lens.
(B) S.I unit of the power of a lens is dioptre while focal length is in centimetres — Incorrect. The dioptre is correct, but the SI unit of focal length is the metre, because \( 1\,\mathrm{D} = 1\,\mathrm{m^{-1}} \).
(C) For a lens of larger focal length, power is smaller — Correct. \( P = 1/f \), so the power is inversely proportional to the focal length.
(D) In any combination of lenses, the power of combination is not algebraic addition of power of combined lenses — Incorrect. For lenses in contact the powers add algebraically, \( P = P_1 + P_2 + \dots \).
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.”
Power of a Lens – “… Thus,
\( \displaystyle P = \frac{1}{f} \qquad (9.25) \)
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.”
Combination of Thin Lenses in Contact – “… Note that the sum in Eq. (9.32) is an algebraic sum of individual powers, so some of the terms on the right side may be positive (for convex lenses) and some negative (for concave lenses).”