Question #43612

Two broad, coherent monochromatic light beams, each of wavelength $\lambda$ and uniform intensity $I_0$ (defined as power per unit area perpendicular to the direction of propagation), are incident on a flat photosensitive plate lying in the $x-y$ plane. The wave vectors of the two beams lie in the $x-z$ plane and make angles of $+\theta$ and $-\theta$ with the $z$-axis (which is normal to the plate). The beams are polarized with their electric fields parallel to the $y$-axis, and are in phase at the origin $(0,0,0)$. A rectangular photosensitive strip of width $w$ (along the $y$-axis) and length $L = \frac{\lambda}{6 \sin\theta}$ (along the $x$-axis) is marked on the plate from $x=0$ to $x=L$. The work function of the strip is $\phi$ (where $\phi < hc/\lambda$), and its quantum efficiency is $\eta$ (number of photoelectrons emitted per incident photon). Assuming all emitted photoelectrons are collected, what is the total photoelectric current $i$ generated by the strip? (Here $e$ is the elementary charge, $h$ is Planck's constant, and $c$ is the speed of light)