A point object is placed at a distance of 20 cm from a spherical lens of refractive index $n=\frac{3}{2}$ and the radius of curvature of each surface 10 cm. The distance of the image formed from the lens is

20 cm

The correct answer is Option (3) → 20 cm

Solution:

Using the Lens Maker's Formula:

$\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

Here: $n=\frac{3}{2},\; R_1=+10,\; R_2=-10$

$\frac{1}{f}=\left(\frac{1}{2}\right)\left(\frac{1}{10}-\frac{-1}{10}\right)$

$\frac{1}{f}=\frac{1}{2}\left(\frac{2}{10}\right)=\frac{1}{10}$

$f=10 \; cm$

Now, lens formula:

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{-20}=\frac{1}{10}$

$\frac{1}{v}+\frac{1}{20}=\frac{1}{10}$

$\frac{1}{v}=\frac{1}{10}-\frac{1}{20}=\frac{1}{20}$

$v=20 \; cm$

Distance of the image from the lens = 20 cm