Captain Jack Sparrow tries to observe a fish almost vertically below him in a magical sea of variable refractive index $\mu = y^2 + 1$,where $y$ is the depth below the water surface. Find the apparent depth of the fish below the water level as seen by Captain Jack Sparrow. The actual depth of the fish is $1 \ m$.

$A$ ray of light travelling through glass of refractive index $\sqrt{2}$ is incident on a glass-air boundary at an angle of incidence of $45^{\circ}$. If the refractive index of air is $1$,then the angle of refraction will be: $[\sin 45^{\circ} = \frac{1}{\sqrt{2}}, \sin 90^{\circ} = 1]$ (in $^{\circ}$)

$A$ beam of white light is partially reflected and partially refracted from a surface. The angle between the reflected and refracted light is $90^{\circ}$. The angle of refraction is $30^{\circ}$. The angle of incidence must be (in $^{\circ}$)

An observer can see through a pin-hole the top end of a thin rod of height $h$,placed as shown in the figure. The beaker height is $3h$ and its radius is $h$. When the beaker is filled with a liquid up to a height $2h$,the observer can see the lower end of the rod. Then the refractive index of the liquid is

$A$ rectangular block is composed of three different glass prisms (with refractive indices $\mu_1, \mu_2$ and $\mu_3$) as shown in the figure below. $A$ ray of light incident normal to the left face emerges normal to the right face. Then,the refractive indices are related by

Immiscible transparent liquids $A, B, C, D$ and $E$ are placed in a rectangular glass container,forming layers based on their densities. The refractive indices of the liquids are given in the table below. The container is illuminated from the side,and a small piece of glass with a refractive index of $1.61$ is gently dropped into the liquid layers. In which liquid will the glass piece not be visible as it descends?
| Liquid | Refractive Index |
| :--- | :--- |
| $A$ | $1.51$ |
| $B$ | $1.53$ |
| $C$ | $1.61$ |
| $D$ | $1.52$ |
| $E$ | $1.65$ |