A glass beaker is filled with water up to $5 \mathrm{cm}$. It is kept on top of a $2 \mathrm{cm}$ thick glass slab. When a coin at the bottom of the glass slab is viewed at the normal incidence from above the beaker, its apparent depth from the water surface is $d \mathrm{cm}$. Value of $d$ is close to (the refractive indices of water and glass are $1.33$ and $1.50$ respectively)

Two thin slabs of refractive indices ${\mathrm{\mu }}_1$ and ${\mathrm{\mu }}_2$ are placed parallel to each other in the $\mathrm{x}-\mathrm{y}$ plane. If the direction of propagation of a ray the two media are along the unit vectors ${\hat{\mathrm{r}}}_1=\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}$ and ${\hat{\mathrm{r}}}_2=\mathrm{c}\hat{\mathrm{i}}+\mathrm{d}\hat{\mathrm{j}}$ then we have 

For a small air bubble, located $4 \mathrm{cm}$ below inside a glass sphere (Refractive index$\mu =1.5$) of radius $10 \mathrm{cm}$ is viewed normally from outside as shown in the figure below. Find the apparent depth (aproximately) of the bubble.

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 $E$ ?

In the given figure, if object is placed at a distance of $9 \mathrm{cm}$ from $O_1$, then find the image distance $\left(\mathrm{in} \mathrm{cm} \right)$ from $O_2$•