Question

The dimensional formula for relative refractive index is-
(A)\[\left[ {{M^1}{L^1}{T^{ - 1}}} \right]\]
(B) \[\left[ {{M^0}{L^0}{T^0}} \right]\]
(C) \[\left[ {{M^1}{L^0}{T^0}} \right]\]
(D) \[\left[ {{M^1}{L^1}{T^{ - 1}}} \right]\]

Answer 1

Hint: When light travels from one medium to another medium then the refractive index is known as the relative refractive index whereas When light travels from vacuum to another medium, then the refractive index is known as the absolute refractive index.

Complete step by step answer: refractive index of a medium is defined as the ratio of speed of light in vacuum to the speed of light in medium.
So, \[n = \dfrac{c}{v}\]
Where \[n\]is the refractive index, \[c\]is the speed of light in vacuum and \[v\] is the speed of light in medium.
When light travels from one medium to another then the refractive index is known as the relative refractive index. It is denoted by \[{\mu _r}\] .
As we put values of dimensions in the formula of relative Refractive index then we know both are speeds, Then both will cancel out.
\[{\mu _r} = \dfrac{\mu }{{{\mu _0}}}\]
Here, \[{\mu _r}\] is the relative refractive index and \[\mu \] is the refractive index of the medium and \[{\mu _0}\] is the refractive index of vacuum. and we will get the refractive index as a dimensionless quantity which means \[\left[ {{M^0}{L^0}{T^0}} \right]\]. There will be no mass, length and time term so its dimensions will be zero.

So, option(B) is correct.

Note: Refractive index of vacuum or air is 1. A refractive index is the ratio of speeds of light in different mediums. So, it has no units and it is a dimensionless quantity. It must be kept in mind that whenever we talk about relatives of any term, in most of the cases we would end up with dimensionless parameters.