NDA (II) 2024 GAT Q121: Which one among the following is the correct focal length

Q: What is the answer to NDA (II) 2024 GAT Q121?

C. Correct — C, +2.0 m. Lens powers add algebraically: the combined power P = P1 + P2 = 2.5 D + (-2.0 D) = +0.5 D. The focal length is the reciprocal of the power in metres, f = 1/P = 1/0.5 = +2.0 m. The positive sign shows the combination behaves as a converging (convex) lens. (Provisional — pending the official UPSC key.)

NDA (II) 2024 General Ability Test · Question 121 of 141

Question text verified against the official NDA question paper.

Provisional answers. UPSC has not yet released the official NDA 2024 answer key (it is published several months after the exam). The answers here are our best-supported answers — derived from careful subject-solving and cross-checked against independent solved papers and primary sources — and will be reconciled to the official key as soon as UPSC publishes it. They are not the official UPSC answer key.

Which one among the following is the correct focal length of a combination of lenses of power 2.5 D and -2.0 D?

(a)+0.5 m
(b)-0.5 m
(c)+2.0 m
(d)-2.0 m

Answer

Why

Correct — C, +2.0 m. Lens powers add algebraically: the combined power P = P1 + P2 = 2.5 D + (-2.0 D) = +0.5 D. The focal length is the reciprocal of the power in metres, f = 1/P = 1/0.5 = +2.0 m. The positive sign shows the combination behaves as a converging (convex) lens.

Why the others are wrong

(a)+0.5 m — This wrongly takes 0.5 as the focal length; 0.5 is the combined power in dioptres, and f = 1/P = 1/0.5 = 2.0 m, not 0.5 m.
(b)-0.5 m — Doubly wrong — it uses 0.5 as a focal length and makes it negative, whereas the net power is positive (+0.5 D).
(d)-2.0 m — The magnitude 2.0 m is right, but the sign is wrong: the net power is +0.5 D (converging), so the focal length is +2.0 m, not -2.0 m.

Concept

The power of a lens is P = 1/f, measured in dioptres (D) when f is in metres; a converging (convex) lens has positive power and a diverging (concave) lens negative power. For thin lenses placed in contact the powers simply add: P = P1 + P2, and the resultant focal length is f = 1/P.

First add the powers (2.5 + (-2.0) = 0.5 D), then invert to get the focal length (f = 1/0.5 = 2.0 m). Because the result is positive, the pair acts as a converging lens — pointing to +2.0 m.

Key facts

Power P = 1/f (f in metres); its unit is the dioptre (D).
For thin lenses in contact, powers add: P = P1 + P2.
Here P = 2.5 + (-2.0) = 0.5 D, so f = 1/0.5 = +2.0 m.
Positive power/focal length means a converging (convex) lens; negative means a diverging (concave) lens.

Study next

Power of a lens and the dioptreCombination of thin lenses in contactSign convention for lenses (convex positive, concave negative)Lens formula 1/f = 1/v - 1/u and magnificationCorrecting eye defects (myopia, hypermetropia) with lenses

Common traps

Forgetting to invert power to get focal length (0.5 D gives 2.0 m, not 0.5 m).
Dropping the sign — a net positive power means a positive (converging) focal length.
Subtracting the powers instead of adding them algebraically.

Exams give two lens powers and ask for the combined power or focal length — add the powers (with sign) and take the reciprocal for f.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
The power of a lens of focal length 50 cm is:
- (a)0.5 D
- (b)2 D
- (c)5 D
- (d)50 D
Answer(b) 2 D — P = 1/f = 1/0.5 m = 2 dioptres.
practice — not a real PYQ
Two thin lenses of powers +3 D and -1 D are placed in contact. The power of the combination is:
- (a)+2 D
- (b)-2 D
- (c)+4 D
- (d)+3 D
Answer(a) +2 D — powers add: 3 + (-1) = +2 D.