When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $5 \ cm$ is the same as in a water column of height $6 \ cm$. If the refractive index of glass is $1.56$,then the refractive index of water is:

$A$ ray of light is incident from air on a glass plate having thickness $\sqrt{3} \, cm$ and refractive index $\sqrt{2}$. The angle of incidence of the ray is equal to the critical angle for the glass-air interface. The lateral displacement of the ray when it passes through the plate is $....... \times 10^{-2} \, cm$ (given $\sin 15^{\circ} = 0.26$).

$A$ vessel of depth $2h$ is half-filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be:

Pick out the wrong statement from the following:

$A$ glass slab of thickness $3 \, cm$ and refractive index $3/2$ is placed on an ink mark on a piece of paper. For a person looking at the mark from a distance of $5.0 \, cm$ above the slab,the distance of the mark will appear to be.....$cm$.

How much water should be filled in a container $21 \ cm$ in height,so that it appears half-filled when viewed from the top of the container? (Given that refractive index of water $\mu = 4/3$)