Question

The Young's double slit experiment is done in a medium of refractive index 4/3. A light of 600 nm wavelength is falling on the slits have 0.45 mm separation. The lower slit $S_2$ is covered by a thin glass sheet of thickness 10.4 mm and refractive index 1.5. The interference pattern is observed on a screen placed at 1.5 m from the slits as shown in the fig.
(All wavelength in this problem are for the given medium of refractive index 4/3. Ignore dispersion.) Find the location of central maxima (bring fringe with zero path difference ) on the y-axis.

Answer 1

$d=0.45\times {10}^{-3}mD=1.5mt=10.4\times {10}^{-3}m{\mu }_{med}=\frac{4}{3}{\mu }_{glass}=1.5\Delta x_1=S_{1}P-S_{2}P=\frac{yd}{D}$

Path difference due to glass sheet

$\Delta x_2=(\frac{{\mu }_{glass}}{{\mu }_{med}}-1)t$

For central maximum $\Delta x_1=\Delta x_2$

$\frac{yd}{D}=(\frac{{\mu }_{glass}}{{\mu }_{med}}-1)t\Rightarrow y=4.33m$