$A$ bubble in a glass slab (refractive index $1.5$) when viewed from one side appears at $5 \,cm$ and at $2 \,cm$ from the other side. Then the thickness of the slab is: (in $\,cm$)

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. . . . .

Some water is filled in a container of height $30 \, cm$. If it is to appear half-filled to the observer when viewed from the top of the container, the height up to which water should be filled in it is [Refractive index of water $= \frac{4}{3}$] (in $cm$)

In the given diagram,the apparent velocity of a bird (coming toward a fish) as seen by the fish is $19 \, cm/s$. Find the actual velocity of the bird in $cm/s$.

$A$ vessel of depth $2h$ is half-filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be:

Two parallel rays of red and violet colour pass through a glass slab. Which of the following is correct?