Question

Given two counter propagating monochromatic electromagnetic plane waves with equal strength and frequency but orthoganal polarization, (one is y polarized, the other is z polarized). More specifically, the z polarized wave is traveling in the positive x direction and the y polarized wave is traveling in the negative x direction. show that the polarization of the electric field changes along the x axis.

Answer 1

The z-polarized wave would be of the form
\[E_0 e^{i(kx - \omega t)} \hat{z} \]
and the y polarized wave would look like
\[E_0 e^{i(kx + \omega t)} \hat{y}\]
so what is their sum?

Answer 2

sure, you add them up you get a vector, but how do you show that the polarization changes along the x axis? I don't think i really understand the question.

Answer 3

You could show for instance that the sum of the two is
\[E_0 e^{ikx} \left( e^{-i \omega t} \hat{z} + e^{i\omega t} \hat{y}\right) \]
\[ = E_0e^{i(kx - \omega t)}\left(\hat{z} + e^{2i\omega t}\hat{y} \right) \]
That's a wave but its polarization is kind of weird... can you visualize it?