A uniform plane wave $1$

$$ j yinc

x oE e

$$

$=$E a propagating in a dielectric medium with relative permittivity

$14$r

$=$ is normally incident on a planar boundary in the y$=0$ plane separating a second medium with

relative permittivity $216.$r

$=$ Determine,

a$)$ The incident magnetic field.

b$)$ Write down expressions for the reflected and transmitted fields that satisfy the wave equation.

c$)$ Solve for the amplitude of the reflected and transmitted fields as a scaling of oE $.$

$($Answer: a$)1$

$1$

$$ j yinc o

z

E e

$$

$=$H a $,$ b$)12$

$,$j y j yref trans

x o x oE e E e

$+$

$==$E a E a $,$

c$)12$

$,$

$33$

o o o oE E E E

$==)$