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  4. Suppose refractive index μ is given as μ = A + (B/λ2) where A and B are constants and λ is wavelength, then dimensions of B are same as that of

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

JIPMERJIPMER 2015Physical World, Units and Measurements

Solution:

$ \mu = \frac { velocity \, of \, light \, in \, vacuum }{ velocity \, of \, light \, in \, medium } $
The refractive index $ \mu$ is dimensionless, so each term on right hand side is dimensionless. Hence, $ \frac{ B }{ \lambda^2 }$ is dimensionless.
This implies that dimensions of B will have the dimensions of
$ \lambda^2 $ ie, of area. ie, of $cm^2$ or area.