$[9]($difficulty: average$)$

Figure depicts a case of oblique incidence on an interface between two lossless media. The incident wave is polarized perpendicular to the plane of incidence $($the plane determined by the incident Poynting vector and the normal to the interface$).$ The plane of incidence is here referred to two cartesian coordinate systems, $xy$ and $x^{\text{'}}{y}^{\text{'}}.$

Fig.

Assuming that the incident $E-$field is given by $E_i=E_0{e}^{j{}_1{x}^{\text{'}}}{a}_{z^{\text{'}}},$ express $E_i$ and $H_i$ in the $($a$)(x,y,z)$ coordinate system.

$($b$)$ Write boundary conditions for the fields of Problem