$A$ 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

$A$ glass slab consists of thin uniform layers of progressively decreasing refractive indices $(RI)$ such that the $RI$ of any layer is $\mu - m \Delta \mu$. Here, $\mu$ and $\Delta \mu$ denote the $RI$ of the $0^{\text{th}}$ layer and the difference in $RI$ between any two consecutive layers, respectively. The integer $m = 0, 1, 2, 3, \ldots$ denotes the number of the successive layers. $A$ ray of light from the $0^{\text{th}}$ layer enters the $1^{\text{st}}$ layer at an angle of incidence of $30^{\circ}$. After undergoing the $m^{\text{th}}$ refraction, the ray emerges parallel to the interface. If $\mu = 1.5$ and $\Delta \mu = 0.015$, the value of $m$ is:

$A$ 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 $\mu = 4/3$).

$A$,$B$ and $C$ are parallel-sided transparent media of refractive indices $n_{1}$,$n_{2}$ and $n_{3}$ respectively. They are arranged as shown in the figure. $A$ ray is incident at an angle $i$ on the surface of separation of $A$ and $B$. After refraction into medium $B$,the ray grazes the surface of separation of media $B$ and $C$. Then,$\sin i$ equals to

The refractive index of water and glass with respect to air is $1.3$ and $1.5$ respectively. Then the refractive index of glass with respect to water is

$A$ ray of light $AO$ in vacuum is incident on a glass slab at an angle of $60^o$ and refracted at an angle of $30^o$ along $OB$ as shown in the figure. The optical path length of the light ray from $A$ to $B$ is