$A$ light ray travels from a medium with refractive index $n_1$ to another medium of refractive index $n_2$. If $n_1=2$ and $n_2=\sqrt{3}$, then find the critical angle. (in $^{\circ}$)

$A$ jar of height $h$ is filled with a transparent liquid of refractive index $\mu$. At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of a disc,such that when placed on the top surface symmetrically about the centre,the dot is invisible.

An endoscope is employed by a physician to view the internal parts of a body organ. It is based on the principle of

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 ${\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$.

$A$ ray of light in a liquid of refractive index $1.4$ approaches the boundary surface between the liquid and air at an angle of incidence whose sine is $0.8$. Which of the following statements is correct about the behavior of the light?

In the figure shown,for an angle of incidence $i$ at the top surface,the minimum refractive index $\mu$ needed for total internal reflection at the vertical surface will be