Question

The graph between $\frac 1u$ and $\frac 1v$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5, and its both the surfaces have the same radius of curvature R. The value of R will be______cm.
(where u = object distance, v = image distance)

Answer 1

Focus $f=10\ cm$
$\frac 1f=(μ−1)(\frac 1R−\frac {1}{−R})$

$\frac {1}{10}=\frac {1.5−1}{1}×\frac 2R$

$\frac {1}{10}=\frac {0.5×2}{R}$

$\frac {1}{10}=\frac 1R$

$R=10\ cm$

So, the answer is $10\ cm.$