Q59 / 75 · JEE Main 2026 (24 January Shift 2) · Physics
Five persons $\mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}, \mathrm{P}_{4}$ and $\mathrm{P}_{5}$ recorded object distance $(\mathrm{u})$ 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
- AReadings recorded by $\mathrm{P}_{3}$ and $\mathrm{P}_{2}$ persons are incorrect
- BReadings recorded by $P_{4}$ and $P_{5}$ persons are incorrect
- CReadings recorded by all persons are correct
- Correct answerDReadings recorded by $\mathrm{P}_{3}$ person are incorrect
Solution
For a convex lens with power $P = +5$ D, the focal length is $f = 20$ cm.
The lens formula is $\frac{1}{f} = \frac{1}{u} + \frac{1}{v} = 0.05$ cm$^{-1}$. Checking each measurement:
$P_1$: $\frac{1}{25} + \frac{1}{96} = 0.0504$ Correct;
$P_2$: $\frac{1}{30} + \frac{1}{62} = 0.0494$ Correct;
$P_3$: $\frac{1}{35} + \frac{1}{37} = 0.0556$ Incorrect;
$P_4$: $\frac{1}{45} + \frac{1}{35} = 0.0508$ Correct;
$P_5$: $\frac{1}{50} + \frac{1}{32} = 0.0512$ Correct.
Only $P_3$'s readings do not satisfy the lens formula.
The lens formula is $\frac{1}{f} = \frac{1}{u} + \frac{1}{v} = 0.05$ cm$^{-1}$. Checking each measurement:
$P_1$: $\frac{1}{25} + \frac{1}{96} = 0.0504$ Correct;
$P_2$: $\frac{1}{30} + \frac{1}{62} = 0.0494$ Correct;
$P_3$: $\frac{1}{35} + \frac{1}{37} = 0.0556$ Incorrect;
$P_4$: $\frac{1}{45} + \frac{1}{35} = 0.0508$ Correct;
$P_5$: $\frac{1}{50} + \frac{1}{32} = 0.0512$ Correct.
Only $P_3$'s readings do not satisfy the lens formula.
Hence, the correct answer is option: 'D'.