What will be the minimum angle of incidence $i$ such that total internal reflection takes place at both interfaces (in $^{\circ}$)? (Given: $\mu_1 = \sqrt{2}, \mu_2 = 2, \mu_3 = \sqrt{3}$)

For total internal reflection to occur, which one of the following is the correct statement? $(i = \text{angle of incidence}, i_{C} = \text{critical angle})$.

$A$ diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $\frac{4}{3}$,and the diver's eyes are $15 \, cm$ below the surface of water. Then the radius of the circle is

Material $A$ has a critical angle ${i_A},$ and material $B$ has a critical angle ${i_B}$ $({i_B} > {i_A})$. Then which of the following is true?
$(i)$ Light can be totally internally reflected when it passes from $B$ to $A$.
$(ii)$ Light can be totally internally reflected when it passes from $A$ to $B$.
$(iii)$ The critical angle for total internal reflection is ${i_B} - {i_A}$.
$(iv)$ The critical angle between $A$ and $B$ is ${\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$.

$A$ water-proof laser pointer of length $10 \,cm$ is placed in a water tank. It rotates about a horizontal axis passing through its centre of mass in a vertical plane as shown in the figure. The time period of rotation is $60 \,s$. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to ............. $s$. (Take, refractive index of water $= 1.33$)

$A$ beam containing red,green,and blue light is incident on a prism. Their refractive indices are $1.39, 1.44$,and $1.47$ respectively. Then,the prism: