Question #43726

In a modified Young's Double Slit Experiment, a monochromatic light source of wavelength $\lambda$ (in m) illuminates a narrow source slit $S$. The light then passes through two narrow slits $S_1$ and $S_2$ separated by a distance $d$ (in m). The distance between the plane of $S$ and the plane of $S_1, S_2$ is $L$ (in m). A screen is placed at a distance $D$ (in m) from the double-slit plane. The source slit $S$ is made to oscillate in simple harmonic motion along an axis parallel to the slit plane and perpendicular to the optical axis. Its displacement from the optical axis is given by $y(t) = A \sin(\omega t)$, where $A$ (in m) is the amplitude and $\omega$ (in rad/s) is the angular frequency. Assume $L \gg d$, $D \gg d$, and $A$ is small such that the maximum path difference introduced is much less than $\lambda$. If $I_0$ (in W/m$^2$) is the intensity at the center of the screen $O$ when $S$ is stationary at the optical axis, what is the fractional decrease in the time-averaged intensity, $\frac{I_0 - \langle I \rangle}{I_0}$, measured by a slow detector at $O$?