Question

Can the absolute refractive index of a medium with respect to another medium be less than unity? Give a reason.

Answer 1

You are asked to determine whether the value of the refractive index of any medium could be less than unity. In order to find an answer to this question, you could recall the expression for absolute refractive index of a medium. You could see whether this statement could possibly be true.

Formula used:
Refractive index,
$n=\dfrac{c}{v}$

Complete step-by-step solution:
In the question, we are asked whether the refractive index of a medium with respect to another medium is less than unity. We are also asked to give a valid reason as justification to support their answer.
As a very first step, one could recall the definition for absolute refractive index. It could be defined as the ratio of velocity of light in vacuum to the velocity of light in any given medium. Let c be the velocity of light in vacuum and v be the velocity of light in a given medium and n be the absolute refractive index of the medium then,
$n=\dfrac{c}{v}$
Now, when the absolute refractive index of a medium is less than unity which would imply that the velocity of light in that medium is more than that in vacuum which is impossible as we know that the velocity of light in vacuum is higher than any other medium.
Hence, we could conclude that the absolute refractive index of a medium with respect to another medium cannot be less than unity.

Note: A major conclusion you could make from the value of refractive index is that lower the value of refractive index is the denser that medium would be. Similarly, higher the value of refractive index is rarer that particular medium would be. So, always keep in mind c is the maximum speed of light.