$A$ fish rising vertically up towards the surface of water with speed $3 \; ms^{-1}$ observes a bird diving vertically down towards it with speed $9 \; ms^{-1}$. The actual velocity of the bird is.......$ms^{-1}$ (Assume refractive index of water $\mu = 4/3$).

The refractive index of the material of a crystal is $1.68$ and that of castor oil is $1.2$. When a ray of light passes from oil to the crystal,its velocity will change by a factor of:

An electromagnetic wave,whose wave normal makes an angle of $45^{\circ}$ with the vertical,travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $15^{\circ}$. What is the speed of the electromagnetic wave in the liquid,if the speed of electromagnetic wave in air is $3 \times 10^8 \ m/s$? $(\sin 30^{\circ} = 0.5, \sin 45^{\circ} = \frac{1}{\sqrt{2}})$

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 |
| :--- | :--- |
| $A$ | $1.51$ |
| $B$ | $1.53$ |
| $C$ | $1.61$ |
| $D$ | $1.52$ |
| $E$ | $1.65$ |

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 travels from air to water to glass and again from glass to air. Refractive index of water with respect to air is $x$, glass with respect to water is $y$, and air with respect to glass is $z$. Which one of the following is correct?