# GATE 2015 EE - SET 2 - Question 9

Solution :

Region 1

y <  0 , $\epsilon _{1}$=2

Region 2

y > 0 , $\epsilon _{2}$=5

According to wave propogation ,

1. The parallel components of the dielectric medium will be the same for both . In this case the components $\hat{a_{x}}$ and $\hat{a_{z}}$ will remain the same for  $\vec{E_{1}}$ and  $\vec{E_{2}}$ .
2. The perpendicular components of the dielectric medium will be equal (ratio )

$\epsilon _{1}\vec{E_{1\perp }}$ = $\epsilon _{2}\vec{E_{2\perp }}$  $\Rightarrow$ 2(4$\hat{a_{y}})$

$\Rightarrow$ 5$E_{2\perp }$= $E_{2\perp }$= $\frac{8\hat{a_{y}}}{5}$ = 1.6$\hat{a_{y}}$

$E_{1}$ = 3$\hat{a_{x}} + 4\hat{a_{y}} + 2\hat{a_{z}}$

$E_{2}$ = 3$\hat{a_{x}} + 1.6\hat{a_{y}} + 2\hat{a_{z}}$