If ${ }_{i} \mu_{j}$ represents the refractive index when a ray goes from medium $i$ to medium $j$,then the product ${ }_2 \mu_1 \times { }_3 \mu_2 \times { }_4 \mu_3$ is equal to:

Let the $x-z$ plane be the boundary between two transparent media. Medium $1$ in $z \ge 0$ has a refractive index of $\sqrt{2}$ and medium $2$ with $z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light in medium $1$ given by the vector $\overrightarrow{A} = 6\sqrt{3} \widehat{i} + 8\sqrt{3} \widehat{j} - 10\widehat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is ......$^o$.

Electromagnetic radiation of frequency $n$,wavelength $\lambda$,travelling with velocity $v$ in air,enters a glass slab of refractive index $\mu$. The frequency,wavelength,and velocity of light in the glass slab will be respectively:

$(a)$ The refractive index of glass is $1.5$. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times 10^{8} \; m/s$).
$(b)$ Is the speed of light in glass independent of the colour of light? If not,which of the two colours,red or violet,travels slower in a glass prism?

Is the statement "Angle made by the incident ray with the reflecting surface is the angle of incidence" correct?

$A$,$B$ 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