Question #43051

In a modified Young's Double Slit Experiment, the entire setup is immersed in a lossy liquid medium. The amplitude of a light wave traveling a distance $x$ in this medium decays as $A(x) = A_0 e^{-\alpha x}$, where $\alpha$ is a positive absorption constant. The slits $S_1$ and $S_2$ are separated by a distance $d$ and are illuminated by coherent light such that the initial amplitudes at the slits are both $A_0$. The screen is placed at a distance $D$ ($D \gg d$). If the wavelength of the light in the medium is $\lambda$, which of the following expressions correctly represents the visibility $V$ of the $n^{\text{th}}$ bright fringe on the screen? \n\n(Assume $y \ll D$ where $y$ is the distance from the central maximum, and define local visibility as $V = \frac{I_{\text{max}} - I_{\text{min}}}{I_{\text{max}} + I_{\text{min}}}$ where $I_{\text{max}}$ and $I_{\text{min}}$ are the envelope intensities near the $n^{\text{th}}$ fringe.)