In a vessel of $21 \, cm$ depth,up to what height should water be filled so that it appears to be $20\%$ filled when viewed from the top (in $, cm$)? (Given: $\mu_{water} = 4/3$)

The time required for light to pass through a glass slab of $2 \ mm$ thickness is $({\mu _{glass}} = 1.5)$.

$A$ 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:

$A$ printed page is pressed by a glass of water. The refractive index of the glass and water is $1.5$ and $1.33$,respectively. If the thickness of the bottom of the glass is $1\, cm$ and the depth of the water is $5\, cm$,how much will the page appear to be shifted if viewed from the top (in $,cm$)?

As shown in the figure,a plane mirror is fixed at a height of $50\,cm$ from the bottom of a tank containing water $\left(\mu = \frac{4}{3}\right)$. The height of water in the tank is $8\,cm$. $A$ small bulb is placed at the bottom of the water tank. The distance of the image of the bulb formed by the mirror from the bottom of the tank is $......\,cm$.

What is the time taken (in seconds) for light to cross a glass slab of thickness $4 \ mm$ and refractive index $\mu = 3$?