Question

if meu not is relative permeability and k not is the dielectric constant of a medium its refractive index is given by explain how it came?

Answer 1

$$\begin{gathered} Weknowthatenergystoredinacapacitorisgivenby, \\ U=\frac{1}{2}{\epsilon }_0{E}^{2}andtheenergystoredinaninductor, \\ U=\frac{1}{2}\frac{B^2}{{\mu }_0}.AsthesetwoenergiesareequalincaseE.M.Waves. \\ So,\frac{1}{2}{\epsilon }_0{E}^2=\frac{1}{2}\frac{B^2}{{\mu }_0} \\ or{\left(\frac{E}{B}\right)}^2=\frac{1}{{\epsilon }_0{\mu }_0}. \\ But\frac{E}{B}=c,so{c}^2=\frac{1}{{\epsilon }_0{\mu }_0}. \\ orc=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}---\left(1\right) \\ SIMILARLYv=\frac{1}{\sqrt{\epsilon \mu }}----\left(2\right) \\ fromeqns\left(1\right)and\left(2\right),weget, \\ refractiveindex=\frac{c}{v}=\sqrt{\frac{\epsilon \mu }{{\epsilon }_0{\mu }_0}}=\sqrt{k_0{\mu }_r}. \\ where{\mu }_{r}isrelativepermeability. \end{gathered}$$