Optics - Transmission of plane wave at oblique incidence

[Flexington]

I have 2 questions that need help with,

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 propagation vector of the transmitted wave.

My attempt is that i can resolve the propagation 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 propagation vector depends only on the dielectric constants such that,

K[/SUB]2[/SUB] = 3K¹/2
(K is mag of propagation vector)
However, to express it back in vectorial form I am lost.


Thank you

 

[Flexington]

Ok, so i have the 2nd part regarding the propagation vector. I can use the angle of refraction, from snells law, to find the x and y components of the transmitted waves propagation vector, with the new magnitude 3/2. As the mgnitude in meda one was 1.

Howver i am still baffled with how i can deduce the direction of oscillations of the electric field?

 

[chrisbaird]

The equation you wrote down has no directionality, so it is no wonder you are having a hard time finding it. As written, your equation is not complete. If it were written:

E=x30 (0.866 i + 0.5k)exp{i(-0.5x + 0.866z)}

then the E field would be pointing in the x direction

 

[jtbell]

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?

In (0.866i + 0.5k), I suspect that i and k are unit vectors in the x and z directions respectively. If so, the direction of the indicated sum is given by the usual rules for vector addition.