$A$ ray of light is incident at $30^{\circ}$ from a medium of refractive index $2$ into a medium of refractive index $1$. The angle of refraction is: (in $^{\circ}$)

The apparent depth of water in a cylindrical water tank of diameter $2R \ cm$ is reducing at the rate of $x \ cm/minute$ when water is being drained out at a constant rate. The amount of water drained in $c.c./minute$ is: ($n_1 =$ refractive index of air,$n_2 =$ refractive index of water)

According to the Cartesian sign convention in ray optics,

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 $\sin 30^{\circ} = \frac{1}{2}$.

Calculate the value of $n_{32} \times n_{21} = .... $

In the figure shown,$\frac{\sin i}{\sin r}$ is equal to: