An air bubble in a glass slab with refractive index $1.5$ (near normal incidence) is $5\, cm$ deep when viewed from one surface and $3\, cm$ deep when viewed from the opposite face. The thickness (in $cm$) of the slab is

$A$ large glass slab $\left( \mu = \frac{5}{3} \right)$ of thickness $8 \, cm$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \, cm$. What is the value of $R$? ....... $cm$

The bottom of a container is a glass slab of thickness $4 \ cm$ and refractive index $\mu = 1.5$. The container contains two immiscible liquids $A$ and $B$ of depths $6 \ cm$ and $8 \ cm$ respectively. When a crack at the bottom surface of the glass slab is viewed from above,by what distance (in $cm$) does it appear to be shifted? The refractive indices of $A$ and $B$ are $1.4$ and $1.3$ respectively.

Assume the situation shown in the figure. Water $(\mu_w = 4/3)$ is filled in a beaker up to a height of $10 \, cm$. $A$ plane mirror is fixed at a height of $5 \, cm$ above the water surface. The distance of the image of the object $O$ from the mirror is ...... $cm$.

$A$ fish and a bird are moving as shown in the figure. Find the velocity of the bird as observed by the fish.

Consider three media $P$, $Q$, and $R$ with refractive indices $1$, $1.25$, and $1.5$, respectively. The medium $Q$ having a thickness of $5 \text{ cm}$ is placed between extended media $P$ and $R$. An object $O$ is placed at the centre of medium $Q$. If viewed from medium $P$ near the normal direction, the apparent depth of $O$ is $h_1$. For similar observation from medium $R$, the apparent depth is $h_2$. The value of $|h_1 - h_2|$, in $\text{cm}$, is: