Question

The velocity of light in glass whose refractive index w.r.t air is 1.5 is $ 2 \times 10^8 ms^{-1} $. In a certain liquid, the velocity of light is found to be $ 2.5 \times 10^8 ms^{-1} $. The refractive index of liquid w.r.t air is:
A. 0.8
B. 0.9
C. 1.2
D. 1.33

Answer 1

Hint: The speed of light changes if it enters from one medium to another. Refractive index is a property of the medium which is the measure of how slow the speed of light gets on entering a medium. The refractive index is a unique property of a medium which can be constant or variable. Certain physical quantities like temperature govern the change of refractive index of a material.

Formula used:
 $ \mu= \dfrac cv $
Where $ \mu $ is the refractive index of the medium, c is the speed of light in vacuum and is equal to $ 3 \times 10^{8} ms^{-1} $ and v represents the speed of light in a medium of refractive index $ \mu $ .

Complete step-by-step answer:
Given the speed of light in medium with $ \mu =1.5 $ is $ 2 \times 10^8 ms^{-1} $ . Now using refractive index’s definition, $ \mu= \dfrac cv $
Putting the values in the equation, we get
 $ c = \mu \times v $
Or $ c= 1.5\times 2\times 10^8 = 3\times 10^8 ms^{-1} $
Hence, the speed of light in air is $ 3 \times 10^8 ms^{-1} $ .
Now, for the liquid medium;
 $ \mu= \dfrac cv = \dfrac{3 \times 10^8}{2.5 \times 10^8} = 1.2 $
So, refractive index of liquid medium is 1.2

So, the correct answer is “Option C”.

Additional Information: According to Special theory of Relativity, nothing can move faster than the speed of light, which suggests that refractive index can’t be less than unity. Hence, we can directly scrap options 1 and 2. Also the maximum known refractive index is 2.42 which is of diamond. It’s maximum value has no known range.

Note: Refractive index is a dimensionless quantity which plays an important role in understanding the property of a material. It’s definition is the ratio of speed of light in vacuum to that in a medium. It must be noted that the refractive index of vacuum is unity but that of air is not unity but 1.0003. But for numerical problems, one can assume it to be unity.