JEE Main 2026 · 24 January · evening · Single correct · +4 / −1
Five persons P₁,P₂,P₃,P₄ and P₅ recorded object distance (u) and image distance (v) using same convex lens having power +5 D as (25,96),(30,62),(35,37),(45,35) and (50,32) respectively. Identify correct statement
- (a) Readings recorded by P₃ and P₂ persons are incorrect
- (b) Readings recorded by all persons are correct
- (c) Readings recorded by P₃ person are incorrect
- (d) Readings recorded by P₄ and P₅ persons are incorrect
Answer and solution
Answer (c) Readings recorded by P₃ person are incorrect
Solution
Physics sir · 3 steps
Get f = 20 cm from the power, then check which side of 2f each image must land on.
- Focal length. f = 1/P = 1/5 m = 20 cm, so 2f = 40 cm. For a real object and real image of a convex lens, the distances satisfy 1/v + 1/u = 1/f when u and v are taken as magnitudes.
- The 2f rule. If the object is between f and 2f, the image must form beyond 2f. If the object is beyond 2f, the image must form between f and 2f. So u and v can never both be below 40 cm.
Person u (cm) Recorded v (cm) v = uf/(u - f) (cm) Verdict P₁ 25 96 100 fine, beyond 40 P₂ 30 62 60 fine, beyond 40 P₃ 35 37 46.7 wrong, must exceed 40 P₄ 45 35 36 fine, between 20 and 40 P₅ 50 32 33.3 fine, between 20 and 40 - So. Four readings match the lens formula within a few centimetres of experimental error. Only P₃ records an image inside 40 cm for an object inside 40 cm, which is impossible, so the answer is (c).
The idea to keep. For a convex lens, u and v sit on opposite sides of 2f: one below, one above. Both equal 2f only at the special point. Use this to reject a reading in seconds.
Answer from the NTA final answer key. Solution by PrepWiser.