$2.(25$p$)$ The incident field vector for a plane wave is as follows:

E$($x$,$ y$,$ t$)=12$ cos$($wt $-5$x $-12$y$)$ ex $-5$ cos$($wt $-5$x $-12$y$)$ ey

The wave is moving in air and er$=4.$ Both media are lossless and non$-$magnetic. Accordingly,

a$)$ Determine the values $$of k$1,$k$2,$ $,$ $,$ $.$

b$)$ Write the time domain expressions of the electric field vectors.

c$)$ Determine the Brewster angle.