Question

What is the SI unit of refractive index?
A) $\text{m}{{\text{s}}^{\text{-1}}}$
B) Hz
C) $\overset{\circ }{\mathop{A}}\,$
D) None

Answer 1

Hint: Refractive index of a medium is the ratio of speed of light in vacuum to the speed of light in the given medium.

Complete step by step answer:

Let us first see what is refraction. Refraction is the phenomenon of bending of light when it passes through one medium to another different medium. Which means that when a light ray from one medium enters another medium, it changes its direction.
In addition, when light travels through different mediums, the speed of light changes. We all know that the speed of light $3\times {{10}^{8}}m{{s}^{-1}}$. But this is true only when light is travelling vacuum and this value of speed of light is fastest (i.e. in vacuum). When light from vacuum enters a different medium, its speed decreases and the light changes its direction.
To understand this phenomenon of bending of light, we have something known as a refractive index. Refractive index is the ratio of the speed of light in vacuum to the speed of light in the given medium and it is denoted by $'\mu '$.

Therefore, $\dfrac{c}{v}$

Where ‘c’ is the speed of light in vacuum and ‘v’ is the speed of light in the given medium.
Now, let us check the units of the refractive index. Unit of refractive index ($\mu $) will be the ratio of the unit of speed of light in vacuum(c) to the speed of light in the given medium(v).
Divide unit of c by unit v ;

$\Rightarrow \text{unit of } \!\!\mu\!\!\text{ = }\dfrac{\text{m}{{\text{s}}^{\text{-1}}}}{\text{m}{{\text{s}}^{\text{-1}}}}\text{ = 1}$

As you can see, the unit of refractive is 1, which means the refractive index is just a number without any unit. You can also say that it’s a dimensionless quantity (quantity without any dimensions) since it’s a ratio of two quantities with same dimensions.
Hence, the correct option from the above is (d) none.

Note: It is necessary to remember that the refractive index is $\dfrac{c}{v}$ and not $\dfrac{v}{c}$ since it changes the whole definition of refractive index. Refractive index is always greater than or equal to 1.