In an interferometer with two coherent light sources, the electric fields of the waves are \(\mathbf{E_1} = E_1 \hat{i} e^{i(k_1 z - \omega_1 t)} \)and \(\mathbf{E_2} = E_2 \hat{i} e^{i(k_2 z - \omega_2 t)}\). If the light is monochromatic and the phase difference between the waves is δ=2π, what is the condition for destructive interference?
1
\(\mathbf{k_1} \cdot \mathbf{r} - \omega_1 t = \mathbf{k_2} \cdot \mathbf{r} - \omega_2 t + \pi \)
2
\(\mathbf{k_1} \cdot \mathbf{r} - \omega_1 t = \mathbf{k_2} \cdot \mathbf{r} - \omega_2 t + (2n+1)\pi\)
3
\(\mathbf{k_1} \cdot \mathbf{r} - \omega_1 t = \mathbf{k_2} \cdot \mathbf{r} - \omega_2 t + n\pi \)
4
\(\mathbf{k_1} \cdot \mathbf{r} - \omega_1 t = \mathbf{k_2} \cdot \mathbf{r} - \omega_2 t + 2n\pi\)