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

Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is $6 \,cm$. $A$ coin is placed at the bottom of the beaker. For near normal vision,the apparent depth of the coin is $\frac{\alpha}{4} \,cm$. The value of $\alpha$ is . . . . . . .

When a convex lens is placed above an empty tank,the image of a mark at the bottom of the tank,which is $45 \ cm$ from the lens,is formed $36 \ cm$ above the lens. When a liquid is poured in the tank to a depth of $40 \ cm$,the distance of the image of the mark above the lens is $48 \ cm$. The refractive index of the liquid is

$A$ parallel-sided block of glass with a refractive index of $1.5$ and a thickness of $36 \, mm$ rests on the floor of a tank filled with water (refractive index $= 4/3$). The difference between the apparent depth of the floor at $A$ (where the glass block is present) and $B$ (where only water is present) when seen from vertically above is equal to $....... \, mm$.

Mention the relation between the real depth and the apparent depth in terms of the refractive indices of the media.

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 $4/3$).