Ray Optics

JEE Main level, single correct, medium

172 of 295

Question 172 of 295

A person has been using spectacles of power −1.0-1.0 diopter for distant vision and a separate reading glass of power 2.02.0 diopters. What is the least distance of distinct vision for this person:

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Answer: (D) 50cm50cm

Given, P=2D=2m−1P=2D=2{m}^{-1}
Focal length is 1f=2100cm−1\dfrac{1}{f}=\dfrac{2}{100}{cm}^{-1}
Using lens equation 1v−1u=1f\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}
As we know, u=−25cmu=-25cm
Then, 1v−(−125)=2100\dfrac{1}{v}-\left(-\dfrac{1}{25}\right)=\dfrac{2}{100}
⇒1v=150−125\Rightarrow \dfrac{1}{v}=\dfrac{1}{50}-\dfrac{1}{25}
⇒v=−50cm\Rightarrow v=-50cm

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