Question #76742

In a Young's Double Slit Experiment (YDSE), the slit separation is $d = 1.5 \text{ mm}$ and the screen distance is $D = 2.0 \text{ m}$. A monochromatic light of wavelength $\lambda = 6000 \text{ \AA}$ and intensity $I_0 = 10 \text{ W/m}^2$ is used. A transparent thin film of thickness $t = 15.0 \text{ \mu m}$ and initial refractive index $\mu = 1.50$ is placed in front of one of the slits. The position of the central maximum on the screen is measured using a traveling microscope with a least count of $LC = 0.02 \text{ mm}$. If the refractive index of the film is slowly varied while keeping its thickness strictly constant, what is the minimum change in the refractive index ($\Delta \mu$) that can be confidently detected as a shift in the central maximum by this microscope?