Question #43941

In a modified Young's Double Slit Experiment, a monochromatic light of wavelength $\lambda$ illuminates two identical slits $S_1$ and $S_2$. The slits are mounted on independent mechanical oscillators such that they oscillate along the direction of light propagation (perpendicular to the plane containing the mean positions of the slits). The displacements of the slits from their mean positions are given by $z_1(t) = A \sin(\omega_1 t)$ and $z_2(t) = 2A \sin(\omega_2 t)$, where $A$ is a positive constant. The frequencies $\omega_1$ and $\omega_2$ are non-commensurate, and the observation time is much larger than the time periods of both oscillators. The mean separation between the slits is $d$, and the screen is placed at a large distance $D$ ($D \gg d \gg \lambda$). Assuming $A \ll \lambda$, such that terms of order $(A/\lambda)^4$ and higher can be neglected, what is the visibility $V$ of the time-averaged interference fringes formed on the screen?