# Optics - Transmission of plane wave at oblique incidence

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 Er=2 and second Er=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] = 3K1/2
(K is mag of propogation vector)
However, to express it back in vectorial form im lost.

Thank you

Related Classical Physics News on Phys.org
Ok, so i have the 2nd part regarding the propogation vector. I can use the angle of refraction, from snells law, to find the x and y components of the transmitted waves propogation 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?

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
Mentor
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.