The observer at $O$ views two closely spaced spots on a vertical wall through an angled glass slab as shown. As seen by the observer,the spots appear

$A$ glass cube of length $21 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,its apparent distance is $8 \ cm$. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of the glass and the actual distance of the air bubble from the first surface respectively are:

$A$ layer of oil $3\,cm$ thick is floating on a layer of coloured water $5\,cm$ thick. The refractive index of coloured water is $5/3$ and the apparent depth of the two liquids appears to be $36/7\,cm$. Find the refractive index of oil.

$A$ bubble in a glass slab $(\mu = 1.5)$ when viewed from one side appears at $5 \ cm$ and from the other side appears at $2 \ cm$. The thickness of the slab is .... $cm$.

Consider three media $P$, $Q$, and $R$ with refractive indices $1$, $1.25$, and $1.5$, respectively. The medium $Q$ having a thickness of $5 \text{ cm}$ is placed between extended media $P$ and $R$. An object $O$ is placed at the centre of medium $Q$. If viewed from medium $P$ near the normal direction, the apparent depth of $O$ is $h_1$. For similar observation from medium $R$, the apparent depth is $h_2$. The value of $|h_1 - h_2|$, in $\text{cm}$, is:

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 . . . . . . .