$A$ light ray is incident on a transparent sphere of refractive index $\mu = \sqrt{2}$ at an angle of incidence $i = 45^{\circ}$. What is the total deviation of a ray that enters the sphere,undergoes two internal reflections,and then refracts out into the air (in $^{\circ}$)?

Immiscible transparent liquids $A, B, C, D$ and $E$ are placed in a rectangular glass container,forming layers based on their densities. The refractive indices of the liquids are given in the table below. The container is illuminated from the side,and a small piece of glass with a refractive index of $1.61$ is gently dropped into the liquid layers. In which liquid will the glass piece not be visible as it descends?
| Liquid | Refractive Index |
| :--- | :--- |
| $A$ | $1.51$ |
| $B$ | $1.53$ |
| $C$ | $1.61$ |
| $D$ | $1.52$ |
| $E$ | $1.65$ |

Refractive index of a medium is $\mu$. If the angle of incidence is twice that of the angle of refraction, then the angle of incidence is

$A$ ray of light passes from the vacuum into a medium of refractive index $n$. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is

There are certain materials developed in laboratories which have a negative refractive index. $A$ ray incident from air (medium $1$) into such a medium (medium $2$) shall follow a path given by

$A$ 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 ${\mu _w} = 4/3$):