An extended object of size 2 cm is placed at a distance of 10 cm in air (n = 1) from pole on the principal axis of a spherical curved surface. The medium on the other side of refracting surface has refractive index n = 2. Find the position of image formed after single refraction through the curved surface.

According to question, $u=-10\mathrm{cm}$ 

${\mathrm{\mu }}_1=1, {\mathrm{\mu }}_2=2\text{ and }\mathrm{R}=20\mathrm{cm}$. Let the position of the image from pole be $v.$ 

Using the formula of refraction of light through a spherical surface, we get

$\frac{{\mathrm{\mu }}_2}{\mathrm{v}}-\frac{{\mathrm{\mu }}_1}{\mathrm{u}}=\frac{{\mathrm{\mu }}_2-{\mathrm{\mu }}_1}{\mathrm{R}}$

$\Rightarrow \frac{2}{v}-\frac{1}{-10}=\frac{2-1}{20}=\frac{1}{20}$

$\Rightarrow \frac{2}{v}=\frac{1}{20}-\frac{1}{10}=\frac{-1}{20}$

$\Rightarrow v=-40\mathrm{cm}$

Hence, the image formed is 40 cm from pole  in the medium of refractive index 1.