Question

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:

• A. (A) and (C) only
• B. (B), (C) and (D) only
• C. (A) and (B) only
• D. (A) only

Hint:

The most common mistake related to lens power is the unit of focal length. Always remember that for the power to be in dioptres (the SI unit), the focal length MUST be in meters.

Answer 1

The Correct Option is A

Step 1: Conceptual Understanding:
This question evaluates the definition and characteristics of lens power. Lens power quantifies the degree to which a lens bends light.

Step 2: Detailed Analysis:
(A) The power of a lens denotes its capacity to converge or diverge incident light rays.
This accurately describes lens power qualitatively. A lens with greater power bends light rays more significantly than one with lower power. This statement is correct.
(B) The S.I. unit for lens power is the dioptre, while focal length is measured in centimetres.
The SI unit for power is indeed the dioptre (D). However, power is computed as the reciprocal of the focal length expressed in meters (\(P (\text{in D}) = 1 / f (\text{in m})\)). The assertion that focal length is in centimetres for this calculation is erroneous. This statement is incorrect.
(C) A lens with a longer focal length has lesser power.
As power \(P\) is inversely proportional to focal length \(f\) (\(P = 1/f\)), a lens with a greater focal length will exhibit lower power. This statement is correct.
(D) In any lens combination, the total power is not a simple algebraic sum of individual lens powers.
For thin lenses in contact, the power of the combination is the algebraic sum of their individual powers (\(P_{eq} = P_1 + P_2 + \dots\)). The statement contradicts this by asserting it is *not* an algebraic addition, which is false for this standard configuration. This statement is incorrect.

Step 3: Conclusion:
Only statements (A) and (C) are accurate.