# Homework Help: Problem electromagnetic waves

1. Sep 4, 2010

### Petar Mali

1. The problem statement, all variables and given/known data

Two monocromatic waves is given by

$$\vec{E_1}=\vec{E}_{01}cos(\vec{k}\cdot\vec{r}-\omega t+\alpha_1)$$ and

$$\vec{E_2}=\vec{E}_{02}cos(\vec{k}\cdot\vec{r}-\omega t+\alpha_1)$$

are linearly polarized along two normal directions. Taking that waves have equal amplitude, find polarisation of resultant of this two waves.

2. Relevant equations

3. The attempt at a solution

I suppose that I must try with

$$\vec{E_1}=Re\{\vec{E}_{01}e^{i(\vec{k}\cdot \vec{r}-\omega t+\alpha_1)}\}$$

$$\vec{E_2}=Re\{\vec{E}_{02}e^{i(\vec{k}\cdot \vec{r}-\omega t+\alpha_2)}\}$$

$$\vec{E}=Re\{(\vec{E}_{01}+\vec{E}_{02}e^{i\xi})e^{i(\vec{k}\cdot\vec{r}-\omega t+\alpha_1)}\}$$

where $$\xi=\alpha_2-\alpha_1$$. What now?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution