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Question
Answer the following question.
Define absolute refractive index and relative refractive index. Explain in brief with an illustration for each.
Solution
- 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.
- A stick or pencil kept obliquely in a glass containing water appears broken as its part in water appears to be raised.
- 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.
- 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"` - 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` - Consider a beaker filled with water of absolute refractive index n1 kept on a transparent glass slab of absolute refractive index n2.
- Thus, the refractive index of water with respect to that of glass will be,
gnw = `"n"_2/"n"_1=("c"/"v"_2)/("c"/"v"_1)="v"_1/"v"_2`.
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