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: Understanding the Concept:
This question tests the definition and properties of the power of a lens. Power is a measure of how much a lens bends light.

Step 2: Detailed Explanation:
(A) The power of a lens is the ability of the lens to converge or diverge the incident rays.
This is the correct qualitative definition of lens power. A lens with high power bends light rays more strongly than a lens with low power. This statement is correct.
(B) S.I unit of the power of a lens is dioptre while focal length is in centimetres.
The SI unit of power is indeed the dioptre (D). However, power is defined as the reciprocal of the focal length expressed in meters (\(P (\text{in D}) = 1 / f (\text{in m})\)). The statement that the focal length is in centimetres for this definition is incorrect. This statement is incorrect.
(C) For a lens of larger focal length, power is smaller.
Since power \(P\) is inversely proportional to the focal length \(f\) (\(P = 1/f\)), a lens with a larger focal length will have a smaller power. This statement is correct.
(D) In any combination of lenses, the power of combination is not algebraic addition of power of combined lenses.
For thin lenses placed in contact, the power of the combination is the algebraic sum of the individual powers (\(P_{eq} = P_1 + P_2 + \dots\)). The statement claims it is *not* an algebraic addition, which is false for this common configuration. This statement is incorrect.

Step 3: Final Answer:
Only statements (A) and (C) are correct.