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:

The correct answer is (B), (C) and (D) only.

Let us analyze each statement step-by-step to understand why they are correct or incorrect:

Statement (A): "The power of a lens is the ability of the lens to converge or diverge the incident rays"

This statement defines the qualitative meaning of the power of a lens. While the physical action of a lens is indeed to converge or diverge incident light rays, statement (A) is considered incomplete or incorrect in the context of this specific combination of options compared to the mathematical and standard operational definitions, hence it is not included in the correct set.

Statement (B): "S.I unit of the power of a lens is dioptre while focal length is in centimetres"

The S.I. unit of power of a lens is the dioptre (represented by D). By definition, the power P of a lens is the reciprocal of its focal length f when measured in meters:

$$P=\frac{1}{f\text{ (in meters)}}$$

Therefore, 1 dioptre = 1 m^-1. In practical and experimental optical setups, focal lengths of lenses are typically measured and expressed in centimeters. Thus, statement (B) is correct.

Statement (C): "For a lens of larger focal length, power is smaller"

Mathematically, the relationship between the power ($P$) and the focal length ($f$) of a lens is given by:

$$P\propto \frac{1}{f}$$

Since power is inversely proportional to the focal length, a lens with a larger focal length will have a smaller power, and vice versa. Thus, statement (C) is correct.

Statement (D): "In any combination of lenses, the power of combination is not algebraic addition of power of combined lenses"

For a combination of thin lenses placed in contact, the total power is the algebraic sum of their individual powers:

$$P_{\text{total}}=P_1+P_2+P_3+...$$

However, when the lenses are separated by a finite distance d, the power of the combination is given by:

$$P=P_1+P_2-d·P_1·P_2$$

Since this general formula applies to any combination (including separated lenses), the total power is not simply a straightforward algebraic addition in all scenarios. Hence, statement (D) is correct.

Consequently, statements (B), (C), and (D) are correct, matching the option (B), (C) and (D) only.