Question #43586

A monochromatic light beam of wavelength $\lambda$ illuminates a single slit of width $a$. The resulting diffraction pattern is observed on a screen placed at a distance $D$ ($D \gg a$). A small rectangular photoelectric detector of width $w$ ($w \ll \frac{\lambda D}{a}$) and length $L$ is placed on the screen parallel to the slit. The work function of the detector material is $\phi$ (where $\phi < \frac{hc}{\lambda}$). When the detector is centered exactly at the central maximum of the diffraction pattern, it records a saturation photoelectric current $i_0$ and a stopping potential $V_0$. When the detector is moved and centered exactly at the first diffraction minimum, it records a saturation photoelectric current $i_1$ and a stopping potential $V_1$. Assuming the quantum efficiency of the detector is constant and independent of intensity, which of the following expressions correctly gives $V_1$ and the ratio $\frac{i_1}{i_0}$?