Petar Mali
Sep4-10, 01:45 AM
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
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