Question #91072

In a modified Young's Double Slit Experiment, two coherent point sources $S_1$ and $S_2$ emit light of wavelength $\lambda$. The amplitude of light from $S_1$ decays exponentially with time as $A_1(t) = A_0 e^{-\gamma t}$ (where $\gamma > 0$), while the amplitude of light from $S_2$ remains constant at $A_2(t) = A_0$. At $t=0$, both sources have the same intensity $I_0$. A photographic plate placed on the observation screen is exposed to the interference pattern from $t=0$ to $t = \frac{\ln 2}{\gamma}$. The visibility of the fringes on the developed photographic plate is defined as $V = \frac{E_{max} - E_{min}}{E_{max} + E_{min}}$, where $E$ is the total time-integrated light energy per unit area. Which of the following gives the correct value of $V$?