Question

When a plane wave traveling in free-space is incident normally on a medium having ${ϵ}_r=4.0$, the fraction of power transmitted into the medium is given by

Answer 1

Ans : (a)

$P_t=(1-{\Gamma }^2)P_i$

$\Gamma =\frac{{\eta }_2-{\eta }_1}{{\eta }_2+{\eta }_1}=\frac{\sqrt{\frac{{\mu }_0}{{ϵ}_0{ϵ}_r}}-\sqrt{\frac{{\mu }_0}{{ϵ}_0}}}{\sqrt{\frac{{\mu }_0}{{ϵ}_0{ϵ}_r}}+\sqrt{\frac{{\mu }_0}{{ϵ}_0}}}$

$\Gamma =\frac{\frac{1}{2}-1}{\frac{1}{2}+1}=\frac{-1}{3}$

$\tau =1-{\Gamma }^2=1-\frac{1}{9}=\frac{8}{9}$

$\therefore P_t=\tau .P_i$

$\frac{P_t}{P_i}=\frac{8}{9}$