Question

Prove the relation the refractive index of a medium ‘n’ = (µrεr ) ½ , where µr and εr are the relative permeability and relative permittivity of the medium respectively.

Answer 1

Dear Student,


$$\begin{gathered} speedoflightinvaccum \\ c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}fromEMwaves. \\ speedoflightinothermediumhaving\mu rand\epsilon raretherelativepermeabilityandrelativepermittivity \\ v=\frac{1}{\sqrt{{\mu }_r{\epsilon }_r{\mu }_0{\epsilon }_0}} \\ refractiveindex=\frac{c}{v}=\frac{\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}}{\frac{1}{\sqrt{{\mu }_r{\epsilon }_r{\mu }_0{\epsilon }_0}}}=\sqrt{{\mu }_r{\epsilon }_r} \\ Regards \end{gathered}$$