Ray Optics

JEE Main level, single correct, medium

130 of 295

Question 130 of 295

Five persons P1,P2,P3,P4\mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}, \mathrm{P}_{4} and P5\mathrm{P}_{5} recorded object distance (u)(\mathrm{u}) and image distance (v) using same convex lens having power +5 D as (25,96),(30,62),(35,37),(45,35)(25,96),(30,62),(35,37),(45,35) and (50,32)(50,32) respectively. Identify correct statement

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Answer: (D) Readings recorded by P3\mathrm{P}_{3} person are incorrect

For a convex lens with power P=+5P = +5 D, the focal length is f=20f = 20 cm.
The lens formula is 1f=1u+1v=0.05\frac{1}{f} = \frac{1}{u} + \frac{1}{v} = 0.05 cm−1^{-1}. Checking each measurement:
P1P_1: 125+196=0.0504\frac{1}{25} + \frac{1}{96} = 0.0504 Correct;
P2P_2: 130+162=0.0494\frac{1}{30} + \frac{1}{62} = 0.0494 Correct;
P3P_3: 135+137=0.0556\frac{1}{35} + \frac{1}{37} = 0.0556 Incorrect;
P4P_4: 145+135=0.0508\frac{1}{45} + \frac{1}{35} = 0.0508 Correct;
P5P_5: 150+132=0.0512\frac{1}{50} + \frac{1}{32} = 0.0512 Correct.
Only P3P_3's readings do not satisfy the lens formula.

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