$A$ small pin fixed on a table top is viewed from above from a distance of $50 \, cm$. By what distance would the pin appear to be raised if it is viewed from the same point through a $15 \, cm$ thick glass slab held parallel to the table? (Refractive index of glass $= 1.5$)

$A$ 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:

$A$ 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.....$cm$.

Obtain the relation between the real depth and apparent depth of the bottom of a tank filled with water when observed from air.

$A$ monochromatic light wave is incident normally on a glass slab of thickness $d$,as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$. Which of the following statement$(s)$ is (are) true about the light wave emerging out of the slab?

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