Q 12-09-144JEE MainJEE Main 2022 (26 Jul, Shift 1)Medium
The graph between $\dfrac1u$ and $\dfrac1v$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of the lens is $1.5$ and both its surfaces have the same radius of curvature $R$. The value of $R$ will be ______ cm. (Where $u$ = object distance, $v$ = image distance)
Numerical value type. Enter your answer.
Answer: 10
Lens formula: $\dfrac1v - \dfrac1u = \dfrac1f$. At $A$, $\dfrac1u = 0$ and $\dfrac1v = 0.10\ \text{cm}^{-1}$, so $f = 10\ \text{cm}$ (point $B$ agrees: $0 + 0.10 = 0.10$).
Lens maker's formula: $\dfrac1f = (1.5 - 1)\dfrac2R = \dfrac1R\Rightarrow R = 10\ \text{cm}$.
Solution by Sreeraj P, M.Sc Physics