$A$ coin is placed at the bottom of a glass slab of refractive index $3$ and thickness $x$. Another glass slab of refractive index $\mu$ and thickness $x$ is placed on top of it. If the coin appears to be at the interface of the two slabs,then $\mu = $ . . . . . .

To a bird in air, a fish in water appears to be at $30 \,cm$ from the surface. If the refractive index of water with respect to air is $\frac{4}{3}$, the real depth of the fish from the surface is: (in $\,cm$)

Two transparent slabs have the same thickness $t$. One is made of material $X$ of refractive index $1.5$. The other is made of two materials $Y$ and $Z$ having thicknesses in the ratio $1 : 2$. The refractive index of $Z$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both,the refractive index of $Y$ is

$A$ convex lens with lateral magnification $2$ is used to image a point at the bottom of a tank. The image of the point is formed $60 \ cm$ above the lens. Now a liquid is filled into the tank to a height of $24 \ cm$. It is found that the distance of the image of the same point is now $120 \ cm$ above the lens. Find the refractive index of the liquid.

The bottom of a container is a glass slab of thickness $4 \ cm$ and refractive index $\mu = 1.5$. The container contains two immiscible liquids $A$ and $B$ of depths $6 \ cm$ and $8 \ cm$ respectively. When a crack at the bottom surface of the glass slab is viewed from above,by what distance (in $cm$) does it appear to be shifted? The refractive indices of $A$ and $B$ are $1.4$ and $1.3$ respectively.

$A$ fish and a bird are moving as shown in the figure. Find the velocity of the bird as observed by the fish.