$A$ 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 $\sin 15^{\circ} = 0.26$).

$A$ 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).

$A$ 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

$A$ vessel of depth $d$ is half filled with oil of refractive index $n_1$ and the other half is filled with water of refractive index $n_2$. The apparent depth of this vessel when viewed from above will be

The apparent depth of a needle lying at the bottom of a tank,which is filled with water of refractive index $1.33$ to a height of $12.5\,cm$,is measured by a microscope to be $9.4\,cm$. If water is replaced by a liquid of refractive index $1.5$ up to the same height,what distance would the microscope have to be moved to focus on the needle again (in $,cm$)?

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