Question #43573

Two coherent monochromatic electromagnetic waves, Wave 1 and Wave 2, propagate in a vacuum along the $+z$ direction. Their electric field vectors are given by: ${\vec{E}_1 = E_0 \cos(kz - \omega t) \hat{i}}$ ${\vec{E}_2 = E_0 \cos\left(kz - \omega t + \frac{\pi}{3}\right) \hat{j}}$ where $E_0$ is a constant amplitude in $\text{V/m}$, $k$ is the wave number in $\text{rad/m}$, and $\omega$ is the angular frequency in $\text{rad/s}$. The time-averaged intensity of Wave 1 alone is $I_0$ (in $\text{W/m}^2$). The two waves are superposed, and the resultant wave is incident normally on an ideal linear polarizer. The transmission axis of the polarizer lies in the $xy$-plane and makes an angle of $45^\circ$ with the positive $x$-axis. What is the time-averaged intensity of the transmitted wave?