$(25$ points$)$ A $10$ GHz plane wave propagating in free space is given by Einc $=$y$10$e $$j$(120\mathrm{.}234$x$171\mathrm{.}620$z$)[$V$/$m$].$ This wave is incident on a dielectric half space that begins at z $=0.$ If the relative permittivity of the dielectric half space is $$r $=12,$ answer the following questions. $($a$)(5$ points$)$ What is the angle of incidence of this wave $($measured relative to the z$-$axis$)?($b$)(5$ points$)$ What will the angle of transmission be$?($c$)(5$ points$)$ Find an expression for the incident magnetic field. $($d$)(5$ points$)$ Find an instantaneous expression for the reflected electric field. $($e$)(5$ points$)$ Find an expression for the transmitted electric field.