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

$A$ light beam is traveling from Region $I$ to Region $IV$ (Refer Figure). The refractive indices in Regions $I, II, III$ and $IV$ are $n_0, \frac{n_0}{2}, \frac{n_0}{6}$ and $\frac{n_0}{8}$,respectively. The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is:

Captain Jack Sparrow tries to observe a fish almost vertically below him in a magical sea of variable refractive index $\mu = y^2 + 1$,where $y$ is the depth below the water surface. Find the apparent depth of the fish below the water level as seen by Captain Jack Sparrow. The actual depth of the fish is $1 \ m$.

The velocity of light in glass,whose refractive index with respect to air is $1.5$,is $2 \times 10^8 \ m/s$. In a certain liquid,the velocity of light is found to be $2.5 \times 10^8 \ m/s$. The refractive index of the liquid with respect to air is:

The velocity of light in diamond is $\left(\frac{5}{12}\right)$ times that in air. The velocity of light in water is $\left(\frac{3}{4}\right)$ times that in air. Find the angle of incidence for a ray of light travelling from water to diamond,given that the angle of refraction $r = 30^{\circ}$ and $\sin 30^{\circ} = \frac{1}{2}$.

$A$ rectangular block is composed of three different glass prisms (with refractive indices $\mu_1, \mu_2$ and $\mu_3$) as shown in the figure below. $A$ ray of light incident normal to the left face emerges normal to the right face. Then,the refractive indices are related by