First slide

Dimensions of physical quantities

Question

Suppose refractive index $μ$ is given as $μ = A + \frac{B}{λ^{2}}$ where A and B are constants and $λ$ is wavelength, then dimensions of B are same as that of

Moderate

A

Wavelength
B

Volume
C

Pressure
D

Area

Solution

As $μ = \frac{Velocity of light in vaccum}{Velocity of light in medium}$ hence $μ$ is dimensionless. Thus, each term on the RHS of given equation should be dimensionless, i.e., $B / λ^{2}$ is dimensionless, i.e., B should have dimension of $λ^{2}, i.e., m^{2}$ , i.e., area.

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