Dimensional Formula of Refractive Index

The dimensional formula refractive index is given by,

[M⁰ L⁰ I⁰ T⁰]

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 = [M⁰ L¹ T^-1]

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

⇒ The Refractive Index (n) = [M⁰ L¹ T^-1] × [M⁰ L¹ T^-1]^-1

Therefore, the refractive index is dimensionally represented as [M⁰ L⁰ I⁰ T⁰] = Dimensionless Quantity

⇒ Check Other Dimensional Formulas:

• Dimensions of Time Period
• Dimensions of Dipole Moment
• Dimensions of Rotational Kinetic Energy
• Dimensions of Gravitational Potential Energy
• Dimensions of Impedance

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