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  4. A person has been using spectacles of power -1.0 dioptre for distant vision and a separate reading glass of power 2.0 dioptres. What is the least distance of distinct vision for this person :

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Q. A person has been using spectacles of power $-1.0$ dioptre for distant vision and a separate reading glass of power $2.0$ dioptres. What is the least distance of distinct vision for this person :

JEE MainJEE Main 2023Ray Optics and Optical Instruments

Solution:

$ \frac{1}{ v }-\frac{1}{ u }=\frac{1}{ f } $
$ P =2 D =2 m ^{-1}$
$ \Rightarrow \frac{1}{ f }=\frac{2}{100} \,cm ^{-1} $
$ \frac{1}{ V }-\left(-\frac{1}{25}\right)=\frac{2}{100} $
$ \Rightarrow \frac{1}{ V }=\frac{1}{50}-\frac{1}{25} $
$ \Rightarrow V =-50 \,cm $