Question

A uniform plane wave travelling in free space enters into a lossless medium at normal incidence. In the medium its velocity reduces by 50% and the interface has reflection coefficient of +0.125. The overall permittivity and permeability is

Answer 1

$VelocityOfFreeSpace=v_1=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

$Velocityinmedium=v_2=\frac{1}{\sqrt{\mu \epsilon }}=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0{\mu }_r{\epsilon }_r}}$

According to the question

$\frac{v_2}{v_1}=0.5$

or ${\mu }_r{\epsilon }_r=4$ ...(1)
Also reflection coefficient

$T=\frac{{\eta }_2-{\eta }_1}{{\eta }_2+{\eta }_1}=\frac{\sqrt{\frac{{\mu }_r}{{\epsilon }_r}}-1}{\sqrt{\frac{{\mu }_r}{{\epsilon }_r}}+1}=0.125$

or $\frac{{\mu }_r}{{\epsilon }_r}=1.653$ ....(2)

from (1) and (2)
${\mu }_r=2.571$ and ${\epsilon }_r=1.555$
$\therefore \mu ={\mu }_0{\mu }_r=32.31\times {10}^{-7}H/mand13.76\times {10}^{-12}F/m$