Question
Question: The absolute refractive index of glass and water is \[\dfrac{3}{2}\]and \[\dfrac{4}{3}\], respective...
The absolute refractive index of glass and water is 23and 34, respectively. If the speed of light in glass is 2×108, calculate the speed of light in: a) vacuum b) water
Solution
In this question we have been asked to calculate the speed of light in vacuum and in water. It is given that the refractive index of glass and water is 3/2 and 4/3 respectively. We know that the refractive index is the refractive index in a vacuum. Therefore, using this definition, we shall calculate the speed of light in vacuum and water.
Formula Used:- μ=vc
Where,
μ is the absolute refractive index of the medium
C is the speed of light in a vacuum
V is the speed of light in a medium
Complete step by step solution:
It is given that the absolute refractive index of glass and water is 23and 34, respectively.
Let, absolute refractive index of glass and water be μg and μw
μg=23 and μw=34
It is given that the speed of light in glass vg is 2×108. Therefore, the absolute refractive index of the glass can be given by,
μg=vgc…………. (1)
After substituting the values,
23=2×108c
On solving
We get,
c=3×108
Therefore, the speed of light in vacuum is 3×108.
Now, for the speed of light in water.
It is given the refractive index of water μw=34.
From (1) we can say that refractive index of water is given by,
μw=vwc
After substituting the values,
34=vw3×108
On solving
We get,
vw=2.25×108
Therefore, the speed of light in water is 2.25×108.
Note: The absolute refractive index of a medium is defined as the ratio of the speed of light in the vacuum over the speed of light in the medium. The refractive index of a medium depends on the wavelength of light, optical density, temperature, and refractive index of the surrounding. Impurities present in a medium will increase the refractive index of the medium. As the refractive index of a medium increases its optical density increases. Therefore, the speed of light in that medium is slower.