JEE Main 2026 — Jan 24, Shift 2 — Physics solution

JEE Main2026Jan 24, Shift 2Physics

Five persons $P_{1}, P_{2}, P_{3}, P_{4}$ and $P_{5}$ 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 all persons are correct
B
Reading recorded by $P_{3}$ persons are incorrect
C
Reading recorded by $P_{3}$ and $P_{2}$ persons are incorrect
D
Reading recorded by $P_{4}$ and $P_{5}$ persons are incorrect

Solution

Power $= + 5 D \Rightarrow f = \frac{1}{5} m = 20 cm$ , so $2 f = 40 cm$ .

Standard lens behaviour:

$∙$ If $f < u < 2 f$ (object between 20 and 40 cm), the image lies beyond $2 f$ and is magnified ( $v > 40$ cm, $v > u$ ).

$∙$ If $u > 2 f$ (object beyond 40 cm), the image lies between $f$ and $2 f$ and is diminished ( $20 < v < 40$ , $v < u$ ).

Checking $P_{3}$ : $u = 35$ cm lies between $f$ and $2 f$ , so the image should be beyond 40 cm. But $P_{3}$ records $v = 37$ cm, which is between $f$ and $2 f$ . Inconsistent.

(Lens formula gives $v = 140/3 \approx 46.7$ cm for $u = 35$ cm — far from 37 cm.)

All other readings are qualitatively consistent. So only $P_{3}$ 's reading is incorrect.

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