• # question_answer In Young's double slit experiment with light of wavelength $K=600\text{ }nm,$intensity of central fringe is ${{I}_{0}}$- One of the slits is covered by glass plate of refraction index $1.4$ and thickness $t=5\mu m,$ the new intensity at the same point on screen will be A)  $\frac{{{I}_{0}}}{4}$             B) $\frac{3{{I}_{0}}}{4}$                     C) ${{I}_{0}}$                 D)        $\frac{{{I}_{0}}}{2}$

[a] Optical path diff. $\Delta x=(\mu -1)t$ Phase diff.  $\Delta \phi =\frac{2\pi }{\lambda }\Delta x$ $=\frac{2\pi }{600\times {{10}^{-9}}}\times 0.4\times 5\times {{10}^{-6}}$ $\Delta \phi =\frac{20\pi }{3}$ ${{I}_{res}}={{I}_{0}}{{\cos }^{2}}\left( \frac{\Delta \phi }{2} \right)={{I}_{0}}{{\cos }^{2}}\left( \frac{10\pi }{3} \right)$ $\left[ {{I}_{res}}=\frac{{{I}_{0}}}{4} \right]$