Question

The dimensional formula for refractive index is

• A. $\left[M^0{L}^1{T}^{-1}\right]$
• B. $\left[M^0{L}^0{T}^0\right]$
• C. $\left[M^0{L}^1{T}^1\right]$
• D. $\left[ML{T}^{-1}\right]$

Answer 1

The correct option is B

$\left[M^0{L}^0{T}^0\right]$

Step 1: Use the formula of the refractive index

Know that,

The refractive index = Speed of light in vacuum / Speed of light in the medium

The speed = Distance / Time

Step 2: Calculate the dimensional formula of the refractive index

Therefore the dimensional of the speed $=\left[M^0{L}^1{T}^{-1}\right]$

Now the refractive index

$$\begin{gathered} =\frac{\left[M^0{L}^1{T}^{-1}\right]}{\left[M^0{L}^1{T}^{-1}\right]} \\ =\left[M^0{L}^0{T}^0\right] \end{gathered}$$

Therefore the dimensional of the refractive index is $\left[M^0{L}^0{T}^0\right]$.

Hence, the correct option is (B).