Question

Light travels fastest in
A. Kerosene
B. Turpentine
C. Water
D. All

Answer 1

Hint:Use the formula for the refractive index of a medium. This formula gives the relation between the refractive index of the medium, speed of light in vacuum and speed of light in the medium. From this formula, derive the relation between the refractive index of the medium and speed of light in medium. Hence, conclude in which medium the light will travel faster according to the refractive indices of all the media given in the options.

Formula used:
The refractive index of a medium is given by
\[\mu = \dfrac{c}{v}\] …… (1)
Here, \[\mu \] is the refractive index of the medium, \[c\] is the speed of light in vacuum and \[v\] is the speed of light in the medium.

Complete step by step solution:
We have given three mediums as kerosene, turpentine and water. From equation (1), we can conclude that the speed of light is inversely proportional to the refractive index of the medium and the speed of light in vacuum is constant.
\[v \propto \dfrac{1}{\mu }\]
Hence, the speed of light will be maximum in the medium with lowest refractive index and minimum in the medium with highest refractive index.
The refractive index of kerosene is 1.44.
\[{\mu _K} = 1.44\]
The refractive index of turpentine is 1.47.
\[{\mu _T} = 1.47\]
The refractive index of water is 1.33.
\[{\mu _W} = 1.33\]
We can compare the refractive indices of these three mediums as
\[{\mu _T} > {\mu _K} > {\mu _W}\]
The refractive index of water medium is the least amongst all the given media.Therefore, the light will be travelling fastest in the water medium.

Hence, the correct option is C.

Note:The students should use the formula for refractive index and relation between the refractive index of medium and speed of light in medium carefully. If this relation is not taken correctly, the final answer will be incorrect. Also, if the options vacuum was given in the option, it would be the correct answer as the refractive index of vacuum is the least which is 1.