$A$ rectangular tank of depth $8 \, m$ is full of water $(\mu = 4/3)$. The bottom is seen at an apparent depth of:

$A$ 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

$A$ transparent glass cube of length $24 \,cm$ has a small air bubble trapped inside. When seen normally through one surface from air outside, its apparent distance is $10 \,cm$ from the surface. When seen normally from the opposite surface, its apparent distance is $6 \,cm$. The distance of the air bubble from the first surface is (in $\,cm$)

$A$ 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 $= 1.5$)

The back surface of a glass slab (refractive index $n$ and thickness $t$) is polished to act as a mirror,as shown in the figure. $A$ laser beam is incident on it,which is partially reflected and partially refracted at the air-glass interface. The refracted part is fully reflected at the mirror surface. $A$ pattern of discrete spots of light is observed on a screen placed perpendicular to the glass surface. The spacing between the spots on the screen is:

$A$ glass slab of thickness $4.8 \text{ cm}$ is placed on a piece of paper on which an ink dot is marked. By how much distance would the ink dot appear to be raised (in $\text{ cm}$)? (The refractive index of glass $= 1.5$)