$A$ 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:

$A$ fish rising vertically upward with a uniform velocity of $8\,ms^{-1}$ observes that a bird is diving vertically downward towards the fish with a velocity of $12\,ms^{-1}$. If the refractive index of water is $\frac{4}{3}$,then the actual velocity of the diving bird to pick the fish will be $.......\,ms^{-1}$.

$A$ glass slab of thickness $3 \, cm$ and refractive index $3/2$ is placed on an ink mark on a piece of paper. The mark is viewed from a distance of $5.0 \, cm$ above the top surface of the slab. At what distance (in $cm$) will the mark appear to be?

Time taken by the sunlight to pass through a window of thickness $4 \, mm$ whose refractive index is $1.5$ is

$A$ layer of oil $3\,cm$ thick is floating on a layer of coloured water $5\,cm$ thick. The refractive index of coloured water is $5/3$ and the apparent depth of the two liquids appears to be $36/7\,cm$. Find the refractive index of oil.

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