A thin large film having refractive index μ$$=32$$, is placed in front of slits $$S1$$ and $$S2$$ of Young's double slit experiment such that its thickness varies according to the equation $$t=t0cos25$$$$π$$$$y4d$$ where y $$=$$ $$0$$ is taken at $$S1$$. Find the value of $$t0$$ such that there is central maxima at P (refer$$ $$diagram) Assume Dd

Question

A thin large film having refractive index  μ$$=32$$, is placed in front of slits $$S1$$ and  $$S2$$ of Young's double slit experiment such that its thickness varies according to the equation  $$t=t0cos25$$$$π$$$$y4d$$ where y $$=$$ $$0$$ is taken at  $$S1$$. Find the value of $$t0$$  such that there is central maxima at P (refer$$ $$diagram) Assume  D>>d

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$$t1=t0cos2$$⁡$$0=t0t2=t0cos2$$⁡$$5$$$$π$$$$4d($$−$$d)=t02$$ For central maxima at $$PS2P$$−$$S1P+($$μ−$$1)t2$$−$$t1=0$$⇒$$dxd/2D=32$$−$$1t0$$−$$t02$$⇒$$t0=2d2D$$

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