Question #43574

In a Young's double slit experiment, the distance between the slits is $d = 1.0 \text{ mm}$ and the screen is at a distance $D = 1.0 \text{ m}$ from the slits. A light beam containing two wavelengths $\lambda_1 = 400 \text{ nm}$ and $\lambda_2 = 600 \text{ nm}$ is incident normally on the slits. A thin transparent slab of thickness $t = 2.0 \text{ } \mu\text{m}$ is placed in front of the upper slit. The material of the slab is dispersive, with a refractive index $\mu_1 = 1.60$ for $\lambda_1$ and $\mu_2 = 1.50$ for $\lambda_2$. Find the distance of the point on the screen closest to the geometric center $O$ (the point on the screen opposite to the perpendicular bisector of the slits) where a bright fringe of $\lambda_1$ exactly coincides with a bright fringe of $\lambda_2$.