An electromagnetic wave of intensity $50\ \text{W m}^{-2}$ 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:
Answer: (C) $\left(\sqrt n, \dfrac{1}{\sqrt n}\right)$
For a non-magnetic medium $\varepsilon = n^2\varepsilon_0$ and $v = c/n$. With no loss the intensity is the same:
$$\frac12\varepsilon_0cE_1^2 = \frac12(n^2\varepsilon_0)\frac cnE_2^2 \Rightarrow \frac{E_1}{E_2} = \sqrt n$$
$B = E/v$, so $B_1 = \dfrac{E_1}{c}$ and $B_2 = \dfrac{nE_2}{c}$:
$$\frac{B_1}{B_2} = \frac{E_1}{nE_2} = \frac{\sqrt n}{n} = \frac{1}{\sqrt n}$$
Solution by Sreeraj P, M.Sc Physics