In Young's experiment the upper slit is covered by a thin glass plate of refractive index `1.4` while the lower slit is covered by another glass plate, having the same thickness as the first one but having refractive index `1.7` interference pattern is observed using light of wavelength `5400 Å`
It is found that point P on the screen where the central maximum `(n = 0)` fell before the glass plates were inserted now has `3//4` the original intensity. It is further observed that what used to be the fourth maximum earlier, lies below point P while the fifth minimum lies above P.
Calculate the thickness of glass plate. (Absorption of light by glass plate may be neglected.
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Explanation

After introduction of plates, path difference
`Deltax=[S_(2)P+(mu^(')-1)t]-[S_(1)P+(mu-1)t]`
`=(mu^(')-mu)t=(1.7-1.4)t=0.3t`
Fringe pattern goes below `P`.
Now intensity at `O`, `I_(R)=3/4I_(0)`
`I_(R)=I_(0) cos^(2) (phi//2)`
`(3I_(0))/4=I_(0) cos^(2) (phi//2)implies cosphi//2=sqrt(3)/2=cos pi/6`
`phi=pi/3`
`(2pi)/lambda Deltax=pi/3`
`Deltax=lambda//6, lambda/6+lambda, ...`
Given that previous fifth maximum lies below `P`
(i.e. `Deltaxlt(2xx5+1)lambda/2 impliesDeltaxlt(11lambda)/2`
`Deltax=5lambda+lambda/6`
`0.3t=(32lambda)/6`
`t=(310xx540)/18`
`=9300 nm`
`9.3xx10^(-6) m`