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

 

In a thin spherical fish bowl of radius $10 \mathrm{cm}$ filled with water of refractive index  $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, there is a small fish at a distance of $4 \mathrm{cm}$ from the centre $C$ as shown in the figure. Where will the image of fish appear, if seen from $E$ ?

The observer $O$ sees the distance $AB$ as infinitely large. If the refractive index of the liquid is ${\mu }_1$ and that of glass is ${\mu }_2,$ then $\frac{{\mu }_1}{{\mu }_2}$ is

The first focal length $f_1$ for refraction at a spherical surface is defined as the value of $u$ corresponding to $v=\infty$ (as shown) with refractive indices of two mediums as $n_1$ and $n_2$. The second focal length $f_2$ is defined as value of $v$ for $u=\infty$ (where $R$ is the radius of the curved surface). Choose the correct option(s).

The graph shows how the magnification $m$, produced by a convex thin lens, varies with the image distance $v$. What is the focal length?