$A$ ray of light is incident normally on a glass slab of thickness $5 \ cm$ and refractive index $1.6$. The time taken by a ray to travel from the source to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is: (in $cm$)

$A$ beaker contains water up to a height $h_{1}$ and kerosene of height $h_{2}$ above water. The total height of (water $+$ kerosene) is $(h_{1} + h_{2})$. The refractive index of water is $\mu_{1}$ and that of kerosene is $\mu_{2}$. The apparent shift in the position of the bottom of the beaker when viewed from above is:

$A$ plane glass slab is kept over a coloured word '$VIBGYOR$',where the colour of each letter corresponds to the colours in white light. The letter which appears least raised is

$A$ composite slab consisting of different media is placed in front of a concave mirror of radius of curvature $150 \, cm$. The whole arrangement is placed in water (refractive index $\mu = 4/3$). An object $O$ is placed at a distance $20 \, cm$ from the slab. The refractive indices of the different media are given in the diagram. Find the final image formed by the system.

$A$ ray of light is incident normally on a glass slab of thickness $5 \ cm$ and refractive index $1.6$. The time taken by a ray to travel from the source of light to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is: (in $cm$)

$A$ 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.