$A$ glass slab of thickness $4 \ cm$ contains the same number of waves as $5 \ cm$ of water when both are traversed by the same monochromatic ray of light. The refractive index of water is $4/3$. What is the refractive index of glass?

The lower half of a vessel of depth $2d \text{ cm}$ is filled with a liquid of refractive index $\mu_1$ and the upper half with a liquid of refractive index $\mu_2$. The apparent depth of the vessel seen perpendicularly is

$A$ beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from

$A$ fish at a depth of $12 \, cm$ in water is viewed by an observer on the bank of a lake. To what height the image of the fish is raised? $....... \, cm$ (Refractive index of lake water $= 4/3$)

$A$ transparent cube of $15\, cm$ edge contains a small air bubble. Its apparent depth when viewed through one face is $6\, cm$ and when viewed through the opposite face is $4\, cm$. Then the refractive index of the material of the cube 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. . . . .