Question #43761

In a modified Young's Double Slit Experiment, a primary source placed symmetrically with respect to two narrow slits $S_1$ and $S_2$ emits a single, ultra-short light pulse of duration $\tau$. The pulse has a rectangular time envelope, meaning its intensity is constant for a duration $\tau$ and zero otherwise. The slits are separated by a distance $d$, and the screen is placed at a distance $D$ ($D \gg d$). The intensity of the pulse arriving from each slit individually at the screen is $I_0$.

A detector at a point $P$ on the screen, located at a distance $y$ from the central maximum, measures the total time-integrated energy per unit area (fluence, $F$). If $y$ is such that the path difference $\Delta x = \frac{yd}{D}$ satisfies $0 < \Delta x < c\tau$ (where $c$ is the speed of light in vacuum), which of the following expressions correctly represents the fluence $F$ at point $P$?

(Assume the phase difference between the waves during their overlap is $\Delta \phi = \frac{2\pi yd}{\lambda D}$, where $\lambda$ is the wavelength of the light).