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A parallel beam of monochromatic light o...

A parallel beam of monochromatic light of wacelength `lambda` used in a Young's double slit experiment. The siits are separated by a distance `d` and the screen is placed parallel to the plane of the slits. The incident beam makes an angle `theta=sin^(-1)((lambda)/(2d))` with the normal to the slits. `A` transparent sheet of refractive index `'mu'` and thickness `t=(lambda)/(2(mu-1))` is introduced infront of one of the slit. find the intensity at the geometrical centre.

Text Solution

Verified by Experts

The correct Answer is:
maximum
clearly, at `O`, no defference of path due to inside motion of rays.
only path difference `= S_(1) Q`
`= d cos (90-theta)`
`= d sin theta`.
`= dxx(lambda)/(2d)=(lambda)/(2)`
Net phase difference
so `Deltaphi=(lambda)/(2)xx(2pi)/(lambda)+-(mu-1)t.(2pi)/(lambda)=pi+-(mu-1)(lamda)/(2(mu-1))(2pi)/(lambda)=2pi,0`
`rArr` constructive interference and hence `I_(res)=maxima`
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