$A$ monochromatic ray of light travels through a glass slab and a water column. The number of waves in a glass slab of thickness $4 \ cm$ is the same as in a water column of height $5 \ cm$. If the refractive index of glass is $\frac{5}{3}$,then the refractive index of water 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.

$A$ vessel of depth $2d \ cm$ is half filled with a liquid of refractive index $\mu_1$ and the upper half with a liquid of refractive index $\mu_2$. The apparent depth of the vessel seen perpendicularly is

$A$ coin is placed at the bottom of an empty beaker and is focused by a microscope. When water is poured into the beaker to a height of $10 \, cm$,how much must the microscope be moved to focus it again?

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 $cm$)

An ink mark is made on a piece of paper. $A$ glass slab of thickness $t$ is placed on it. The ink mark appears to be raised up through a distance $x$ when viewed at nearly normal incidence. If the refractive index of the material of the glass slab is $\mu$,then the thickness of the glass slab $t$ is given by: