At the mouth of a cylindrical vessel, a convex lens of refractive index 1.5 and radius of curvature of curved surface 30 cm is filled. A point source S is at the bottom of vessel. The height of vessel is 40 cm and filled with liquid of refractive index 1.2. Find the position of image.

For refraction through spherical surface, ${\mathrm{\mu }}_1=1.2, {\mathrm{\mu }}_2=1.5$

   $\mathrm{r}=+30 \mathrm{cm}, \mathrm{u}=-40 \mathrm{cm}$             

   $\because \frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{r}$             

     Or,  $\frac{1.5}{v}-\frac{1.2}{-40}=\frac{1.5-1.2}{30}\Rightarrow \frac{1.5}{v}+\frac{12}{400}=\frac{3}{300}$

     Or, $\frac{1.5}{v}=\frac{1}{100}-\frac{3}{100}=\frac{-2}{100}$

     Or,  $v=\frac{-100}{2}\times 1.5=-75\mathrm{cm}$

   For refraction through spherical surface, ${\mu }_1^{\text{'}}=1.5, {\mu }_2^{\text{'}}=1, u\text{'}=-75\hspace{0.17em}\mathrm{cm}, r\text{'}=-30$

$\therefore \frac{{\mu }_2^{\text{'}}}{v\text{'}}-\frac{{\mu }_1^{\text{'}}}{u\text{'}}=\frac{{\mu }_2^{\text{'}}-{\mu }_1^{\text{'}}}{r\text{'}}$

Or, $\frac{1}{v\text{'}}+\frac{1.5}{75}=\frac{1-1.5}{-30}$

   $\therefore v\text{'}=-300\mathrm{cm}$