Question

An electromagnetic wave of intensity $50W{m}^2$ enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by :

• A. $(\frac{1}{\sqrt{n}},\frac{1}{\sqrt{n}})$
• B. $(\sqrt{n},\frac{1}{\sqrt{n}})$
• C. $(\sqrt{n},\sqrt{n})$
• D. $(\frac{1}{\sqrt{n}},\sqrt{n})$

Answer 1

Answer: (B)

$(\sqrt{n},\frac{1}{\sqrt{n}})$

$C=\frac{1}{\sqrt{{\mu }_0{\in }_0}}$
$V=\frac{1}{k{\in }_0{\mu }_0}$ [For transparent medium ${\mu }_r\approx {\mu }_0]$
$\therefore \frac{C}{V}=\sqrt{k}=n$
$\frac{1}{2}{\in }_0{E}_0^{2}C=$ intensity =$\frac{1}{2}{\in }_{0}k{E}^{2}v$
$\therefore E_0^{2}C=k{E}^{2}v$
$\Rightarrow \frac{E_0^2}{E^2}=\frac{kV}{C}=\frac{n^2}{n}\Rightarrow \frac{E_0}{E}=\sqrt{n}$
similarly
$\frac{B_0^{2}C}{2{\mu }_0}=\frac{B^{2}v}{2{\mu }_0}\Rightarrow \frac{B_0}{B}=\frac{1}{\sqrt{n}}$