$A$ 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.

$A$ glass slab of thickness $20\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An object is placed at a distance of $40\, cm$ from the mirror in air. The position of the final image with respect to the mirror will be at a distance of:

$A$ glass cube of length $21 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,its apparent distance is $8 \ cm$. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of the glass and the actual distance of the air bubble from the first surface respectively are:

$A$ parallel-sided block of glass with a refractive index of $1.5$ and a thickness of $36 \, mm$ rests on the floor of a tank filled with water (refractive index $= 4/3$). The difference between the apparent depth of the floor at $A$ (where the glass block is present) and $B$ (where only water is present) when seen from vertically above is equal to $....... \, mm$.

An object lying $100 \ cm$ inside water is viewed normally from air. If the refractive index of water is $\frac{4}{3}$,then the apparent depth of the object is (in $cm$)

$A$ glass beaker is filled with water up to $5 \,cm$. It is kept on top of a $2 \,cm$ thick glass slab. When a coin at the bottom of the glass slab is viewed at normal incidence from above the beaker,its apparent depth from the water surface is $d \,cm$. The value of $d$ is close to ........ $cm$ (the refractive indices of water and glass are $1.33$ and $1.5$,respectively).