$A$ glass slab of thickness $6.0 \text{ cm}$ is placed on a piece of paper on which an ink dot is marked. By how much distance would the ink dot appear to be raised (in $\text{ cm}$)? The velocity of light in glass is $2 \times 10^8 \text{ m/s}$ and that in air is $3 \times 10^8 \text{ m/s}$.

Explain the lateral shift for the refraction of light through a rectangular glass slab.

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:

$A$ ray of light is incident on one face of a transparent slab of thickness $15 \, cm$. The angle of incidence is $60^{\circ}$. If the lateral displacement of the ray on emerging from the parallel plane is $5\sqrt{3} \, cm$,the refractive index of the material of the slab is:

An underwater swimmer is at a depth of $12 \, m$ below the surface of water. $A$ bird is at a height of $18 \, m$ from the surface of water,directly above his eyes. For the swimmer,the bird appears to be at a distance from the surface of water equal to ....... $m$ (Refractive index of water is $4/3$).

When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $5 \ cm$ is the same as in a water column of height $6 \ cm$. If the refractive index of glass is $1.56$,then the refractive index of water is: