An underwater swimmer is at a depth of $12 \, m$ below the surface of water. $A$ bird is at a height of $18 \, m$ from the surface of water,directly above his eyes. For the swimmer,the bird appears to be at a distance from the surface of water equal to ....... $m$ (Refractive index of water is $4/3$).

$A$ glass slab of thickness $4 \,cm$ contains the same number of waves as in $x \,cm$ of water column when both are traversed by the same monochromatic light. If the refractive indices of glass and water for that light are $\frac{5}{3}$ and $\frac{4}{3}$ respectively,the value of $x$ will be

$A$ bird is looking at a fish underwater from the air. $h_1$ is the height of the bird above the water surface and $h_2$ is the depth of the fish below the water surface. If $\mu$ is the refractive index of water with respect to air,then the distance of the fish as observed by the bird is:

Consider a configuration of $n$ identical units,each consisting of three layers. The first layer is a column of air of height $h=\frac{1}{3} \text{ cm}$,and the second and third layers are of equal thickness $d=\frac{\sqrt{3}-1}{2} \text{ cm}$,and refractive indices $\mu_1=\sqrt{\frac{3}{2}}$ and $\mu_2=\sqrt{3}$,respectively. $A$ light source $O$ is placed on the top of the first unit,as shown in the figure. $A$ ray of light from $O$ is incident on the second layer of the first unit at an angle of $\theta=60^{\circ}$ to the normal. For a specific value of $n$,the ray of light emerges from the bottom of the configuration at a distance $l=\frac{8}{\sqrt{3}} \text{ cm}$,as shown in the figure. The value of $n$ is. . . . .

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

How much water should be filled in a container $21 \ cm$ in height,so that it appears half-filled when viewed from the top of the container? (Given that refractive index of water $\mu = 4/3$)