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 ......$^o$.

When a light ray is incident on a medium at an angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin r$ vs $\sin i$ is as shown below. From this,one can conclude that:
$(A)$ Velocity of light in the second medium is $1.73$ times the velocity of light in the first medium
$(B)$ Velocity of light in the first medium is $1.73$ times the velocity in the second medium
$(C)$ The critical angle for the two media is given by,$\sin i_c = \frac{1}{\sqrt{3}}$
$(D)$ The critical angle for the two media is given by,$\sin i_c = \frac{1}{2}$

$A$ ray of light is incident at the glass-water interface at an angle $i$. It emerges finally parallel to the surface of water. The value of ${\mu _g}$ is (given refractive index of water ${\mu _w} = 4/3$):

The bottom of a container filled with liquid appears slightly raised because of

$A$ light wave has a frequency of $4 \times 10^{14} \,Hz$ and a wavelength of $5 \times 10^{-7} \,m$ in a medium. The refractive index of the medium is

$A$ 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 $(\mu_W = 4/3) .........$