Question

The dimensional formula for refractive index is,
A. $\left[ {{M}^{0}}{{L}^{1}}{{T}^{-2}} \right]$
B. $\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]$
C. $\left[ {{M}^{0}}{{L}^{1}}{{T}^{1}} \right]$
D. $\left[ {{M}^{1}}{{L}^{1}}{{T}^{-1}} \right]$

Answer 1

Hint: Refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that particular medium. Since the speed of light in vacuum and the speed of light in different mediums have the same dimensions, a quantity which is the ratio of these two will be dimensionless.

Complete step by step answer:
Refractive index of a medium can be expressed as the ratio of the speed of light in vacuum and speed of light in the medium. It is represented as,
$n=\dfrac{c}{v}$
Where,
n is the refractive index of the medium.
v is the velocity of light in that particular medium.
c is the velocity of the light in vacuum.
We can write the dimensional formula of the following ratio, in order to find out the dimensional formula for the refractive index. We know that the dimensional formula for the velocity is $\left[ L{{T}^{-1}} \right]$, which is same for c and v. So, the dimensional formula for refractive index is,
$n=\dfrac{\left[ L{{T}^{-1}} \right]}{\left[ L{{T}^{-1}} \right]}=\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]$
So, we can say that the refractive index is a dimensionless quantity.
So, the answer to the question is option (B).

Note: Refractive index is a measure of the optical density of a medium. The more optically denser a medium is, the less will be the velocity of light in that medium.
Refraction is a process through which light bends away or towards the normal when it travels from one medium to another medium of variable refractive index. The light bent towards the normal if the medium to which it is entering is more optically denser than the first medium. The light bent away from the normal if the medium to which it is entering is less optically denser than the first medium.