$(a)$ Define absolute refractive index.
$(b)$ The path of a light ray from three different media $A, B$ and $C$ for a given angle of incidence is shown below. Study the diagrams and answer the following questions.
$(i)$ Which of the three media $A, B$ or $C$ has maximum optical density?
$(ii)$ Through which of the three media,will the speed of light be maximum?
$(iii)$ Will the light travelling from $A$ to $B$ bend towards or away from the normal?
$(iv)$ Will the refractive index of $B$ relative to $C$ be more than unity or less than unity?

(D) The absolute refractive index of a medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium. Mathematically,$n = c/v$,where $c$ is the speed of light in vacuum and $v$ is the speed of light in the medium.
$(b)$ $(i)$ Optical density is directly related to the refractive index. $A$ higher refractive index means higher optical density. Since the angle of refraction is smallest in medium $C$ $(40^{\circ})$,it has the highest refractive index and thus the maximum optical density.
$(ii)$ The speed of light is inversely proportional to the refractive index. Since medium $A$ has the largest angle of refraction $(50^{\circ})$,it has the lowest refractive index,meaning the speed of light will be maximum in medium $A$.
$(iii)$ Light travelling from $A$ to $B$: Since the angle of refraction in $A$ $(50^{\circ})$ is greater than in $B$ $(45^{\circ})$,medium $B$ is optically denser than medium $A$. Therefore,light will bend towards the normal.
$(iv)$ Refractive index of $B$ relative to $C$ $(n_{BC})$ is given by $n_B / n_C$. Since the angle of refraction in $B$ $(45^{\circ})$ is greater than in $C$ $(40^{\circ})$,medium $C$ is optically denser than $B$ $(n_C > n_B)$. Thus,$n_{BC} = n_B / n_C < 1$,which is less than unity.