Question

The region z<0 and z>0 are nonmagnetic $\mu ={\mu }_0$ perfect dielectrics of permittivities ${\epsilon }_1\text{and}{\epsilon }_2$ respectively. For a uniform plane wave incident from the region z<0 normally onto the boundary z=0. Find the ratio $\frac{{\epsilon }_2}{{\epsilon }_1}$, when the electric field of transmitted wave is six times the electric field of the reflected wave?

• A. $\frac{9}{4}$
• B. $\frac{2}{3}$
• C. $\frac{1}{9}$
• D. $\frac{4}{9}$

Answer 1

The correct option is D $\frac{4}{9}$

$E_1=6E_r$

$\frac{2{\eta }_2}{{\eta }_2+{\eta }_1}=6\left(\frac{{\eta }_2-{\eta }_1}{{\eta }_2+{\eta }_1}\right)$

${\eta }_2=3{\eta }_2-3{\eta }_1$

$3{\eta }_1=2{\eta }_2$

$\frac{{\eta }_1}{{\eta }_2}=\frac{2}{3}\Rightarrow \sqrt{\frac{{\epsilon }_2}{{\epsilon }_1}}=\frac{2}{3}$ $\therefore \frac{{\epsilon }_2}{{\epsilon }_1}=\frac{4}{9}$