Question

Deduce the dimensional formula for refractive Index and frictional force.

Answer 1

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