Question

Answer the following question.

Define absolute refractive index and relative refractive index. Explain in brief with an illustration for each.

Answer 1

1. Absolute refractive index of a medium is defined as the ratio of the speed of light in a vacuum to that in the given medium.
2. A stick or pencil kept obliquely in a glass containing water appears broken as its part in water appears to be raised.
3. As the speed of light is different in two media, the rays of light coming from water undergo refraction at the boundary separating the two media.
4. Consider the speed of light to be v in water and c in air. (Speed of light in air ≈ speed of light in vacuum)
   ∴ refractive index of water = `"n"_"w"/"n"_"a"="n"_"w"/"n"_"vacuum"="c"/"v"`
5. The relative refractive index of a medium 2 is the refractive index of medium 2 with respect to medium 1 and it is defined as the ratio of the speed of light v₁ in medium 1 to its speed v₂ in medium 2.
   ∴ The relative refractive index of medium 2,
   ¹n₂ = `"v"_1/"v"_2`
6. Consider a beaker filled with water of absolute refractive index n₁ kept on a transparent glass slab of absolute refractive index n₂.
7. Thus, the refractive index of water with respect to that of glass will be,
   ^gn_w = `"n"_2/"n"_1=("c"/"v"_2)/("c"/"v"_1)="v"_1/"v"_2`.