$A$ ray of light is incident upon an air/water interface (it passes from air into water) at an angle of $45^o$. Which of the following quantities change as the light enters the water?
$(I)$ wavelength
$(II)$ frequency
$(III)$ speed of propagation
$(IV)$ direction of propagation

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:

Time taken by light to travel in two different materials $A$ and $B$ of refractive indices $\mu_{A}$ and $\mu_{B}$ of the same thickness is $t_{1}$ and $t_{2}$ respectively. If $t_{2}-t_{1}=5 \times 10^{-10} \text{ s}$ and the ratio of $\mu_{A}$ to $\mu_{B}$ is $1:2$. Then the thickness of the material,in meters,is: (Given $v_{A}$ and $v_{B}$ are velocities of light in $A$ and $B$ materials respectively).

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

Monochromatic light of wavelength $589 \; nm$ is incident from air on a water surface. What are the wavelength,frequency,and speed of
$(a)$ reflected,and
$(b)$ refracted light? Refractive index of water is $1.33$.

$A$ pole is vertically submerged in a swimming pool such that it casts a shadow of length $2.15 \, m$ within the water when sunlight is incident at an angle of $30^{\circ}$ with the water surface. If the swimming pool is filled to a height of $1.5 \, m$,then the height of the pole above the water surface in centimeters is $(\mu_W = 4/3) .........$