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  4. The graph between (1/ u ) and (1/ v ) for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of length is 1.5 and its both the surfaces have same radius of curvatures R. The value of R will be cm. (Where u = object distance, v = image distance)

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Q. The graph between $\frac{1}{ u }$ and $\frac{1}{ v }$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of length is $1.5$ and its both the surfaces have same radius of curvatures $R$. The value of $R$ will be ______$cm$.
(Where $u =$ object distance, $v =$ image distance)Physics Question Image

JEE MainJEE Main 2022Ray Optics and Optical Instruments

Solution:

image
For point $ B, \frac{1}{ u }=-0.10\, cm ^{-1}, \frac{1}{ v }=0$
$ \therefore$Thus, $u =-10 \,cm , v =\infty $
i.e. $ f =10 \,cm $
$ \Rightarrow \frac{1}{10 cm }=(1.5-1)\left(\frac{2}{ R }\right)=\frac{1}{ R }$
$ \Rightarrow R =10\, cm$