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Considering the following plane wave,

E= 30 (0.866 i + 0.5k)exp{i(-0.5x + 0.866z)}

firstly how can i deduce the direction of the electric field oscillations?

And finally, if the wave is incident on a dielectric interface between medium of E

_{r}=2 and second E

_{r}=3. How can i find the change in propogation vector of the transmitted wave.

My attempt is that i can resolve the propogation vector from its components in the x and z direction from -0.5x + 0.866z, which gives 60 degrees and that the change in magnitude of the propogation vector depends only on the dielectric constants such that,

K[/SUB]2[/SUB] = 3K

^{1}/2

(K is mag of propogation vector)

However, to express it back in vectorial form im lost.

Thank you