A tiny air bubble inside a glass slab appears to be $6 \mathrm{cm}$ deep when viewed from one side and $4 \mathrm{cm}$ deep when viewed from the other side. Assuming ${\mu }_{glass}=\frac{3}{2}$. Find the thickness of slab in $\mathrm{cm}$.

A rod made of glass $\left(\mu =1.5\right)$ and of square cross-section is bent into the shape shown in figure. A parallel beam of light falls perpendicularly on the plane flat surface $A$. Referring to the diagram, $d$ is the width of a side & $R$ is the radius of inner semicircle. Find the maximum value of ratio $\frac{d}{R}$ so that all light entering the glass through surface $A$ emerge from the glass through surface $B$.

A ray of light falls on a transparent sphere with centre at $C$ as shown in figure. The ray emerges from the sphere parallel to line $AB$. Find the refractive index of the sphere.

A thin equiconvex lens of glass of refractive index $\mu =\frac{3}{2}$ and of focal length $0.3 \mathrm{m}$ in air is sealed into an opening at one end of a tank filled with water $\mu =\frac{4}{3}$. On the opposite side of the lens, a mirror is placed inside the tank on the tank wall perpendicular to the lens axis, as shown in figure. The separation between the lens and the mirror is $0.8 \mathrm{m}$ A small object is placed outside the tank in from of the lens at a distance of $0.9 \mathrm{m}$ from the lens on its axis. Find the position (distance in $\mathrm{cm}$) of the image of the object formed by the systme from the lens).