Question

A slab of a material of refractive index $2$ shown in the figure, has a curved surface $APB$ of radius of curvature $10cm$ and a plane surface $CD$. On the left of $APB$ is air and on the right of $CD$ is water with refractive indices as given in the figure. An object $O$ is placed at a distance of $15cm$ from the pole $P$ as shown. The distance of the final image of $O$ from $P$, as viewed from the left is _______.

Answer 1

For refraction at $APB$,
$-\frac{{\mu }_2}{u}+\frac{{\mu }_1}{v}=\frac{{\mu }_1-{\mu }_2}{R}$
$\Rightarrow \frac{-2}{-15}+\frac{1}{v}=\frac{1-2}{-10}\Rightarrow v^{\prime }=30cm$
$\Rightarrow$ The image $O^{\prime }$ will be formed at $30cm$ to the right at $P$.