# Modern Wave Optics Question

## Homework Statement

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.

## Homework Equations

assume that A=1, ω=2π, k = 2π and let the speed of light c=1

The electric Field is given by the vector E= A <0,sin(-kx-wt),sin(kx-wt)>

## The Attempt at a Solution

I'm not really sure what the question is asking? Do i take derivatives? the curl of the electric field vector? Do i find a time derivative for the Field vector? should I just animate a plot of the electric field strenght? a 3d plot of the field intensity?

## Answers and Replies

rude man
Homework Helper
Gold Member
Just write the equations for planar E waves going in the + and - directions, marking the +x moving wave E field with unit vector z and the -x moving E field with unit vector y.
Let t=0 (or any other arbitrary value) and come up with a vector equation of the compound beam, and show the resultant E vector to be changing in the y-z plane with x. No fancy math required.