Dimensions of Refractive Index

Dimensional Formula of Refractive Index

The dimensional formula refractive index is given by,

[M0 L0 IT0]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Refractive Index (n) = speed of light in vacuum × [speed of light in medium]-1

Since, Speed = Distance × [Time]-1

∴ The dimensional formula of speed = [ML1 T-1]

As the refractive index is the ratio of the speed of light in vacuum and medium.

⇒ The Refractive Index (n) = [ML1 T-1] × [ML1 T-1]-1

Therefore, the refractive index is dimensionally represented as [M0 L0 IT0] = Dimensionless Quantity