$A$ vessel is filled with two different liquids which do not mix. One liquid is $40 \ cm$ deep with a refractive index of $1.6$,and the other is $30 \ cm$ deep with a refractive index of $1.5$. What is the apparent depth of the vessel when viewed normally (in $cm$)?

$A$ large glass slab $\left( \mu = \frac{5}{3} \right)$ of thickness $8 \, cm$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \, cm$. What is the value of $R$? ....... $cm$

$A$ ray of light is incident on a surface of a glass slab at an angle of $45^{\circ}$. If the lateral shift produced per unit thickness is $\frac{1}{\sqrt{3}}$,the angle of refraction produced is

$A$ fish at a depth of $12 \, cm$ in water is viewed by an observer on the bank of a lake. To what height is the image of the fish raised? (Refractive index of water $\mu = 4/3$)

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:

$A$ ray of light is incident on a parallel slab of thickness $t$ and refractive index $n$. If the angle of incidence $\theta$ is small,then the lateral displacement between the incident and emergent ray will be: