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As shown in the figure, in Young's double slit experiment, a thin plate of thicknesst=10\mu m and refractive index t=1.2 is inserted infront of slit S_{1}. The experiment is conducted in air(\mu =1) and uses a monochromatic light of wavelength \lambda =500\; nm. Due to the insertion of the plate, centralmaxima is shifted by a distance of x\beta _{0}.\beta _{0} is the fringe-width befor the insertion of the plate. The value of the x is ________.

Option: 1


Option: 2


Option: 3


Option: 4


Answers (1)


Given\; t=10 \times 10^{-6} \mathrm{~m} \mu=1.2

\lambda=500 \times 10^{-9} \mathrm{~m}

When the glass slab inserted infront of one slit then the shift of central fringe is obtained by

\begin{aligned} & \mathrm{t}=\frac{\mathrm{n} \lambda}{(\mu-1)} \\ & \Rightarrow \quad 10 \times 10^{-6}=\frac{\mathrm{n} \times 500 \times 10^{-9}}{(1.2-1)} \\ & 10 \times 10^{-6}=\frac{\mathrm{n} \times 500 \times 10^{-9}}{0.2} \\ & \mathrm{n}=4 \end{aligned}

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