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 $3 \times 10^8 \ m/s$? $(\sin 30^{\circ} = 0.5, \sin 45^{\circ} = \frac{1}{\sqrt{2}})$

As shown in the figure,after passing through medium $1$,the speed of light $v_{2}$ in medium $2$ will be $..... \times 10^{8} \, ms^{-1}$. (Given $c = 3 \times 10^{8} \, ms^{-1}$)

In the figure shown,the angle made by the light ray with the normal in the medium of refractive index $\sqrt{2}$ is.....$^o$

$A$ beam of light is propagating at an angle $\alpha_1$ from medium $1$ into medium $2$ at an angle $\alpha_2$. If the wavelength of light in medium $1$ is $\lambda_1$, then the wavelength of light in medium $2$, $\lambda_2$, is:

$A$ ray of light travels from air to water to glass and again from glass to air. The 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?

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