A thin glass plate of thickness `t` and refractive index `mu` is between screen &one of the slits in young's experiment.if the intensity at the center of the screen is `I` ,was the intenstity at the same point prior to the introduction of the sheet.
(b) One slit of a young's experiment is covered by a glass plate `(mu_(1)=1.4)` and the other by another glass plate `(mu_(2)=1.7)` of the same thickness. The point of central maxima of the screen,before the plates were introduced is now occupied by the third bright fringe.Find the thicknes of the thickness of the plates.the wavelength of light used in `4000Å`.

Answer

`I_(0)=Isec^(2)[(pi(mu-1)t)/(lambda)]`

Explanation

(a)`I=I_(1)I_(2)+2sqrt(I_(1)I_(2))cosphi`
since`I_(1)=I_(2)=I`
`I=4I_(0)"cos"^(2)(phi)/(2) rArr 4I_(0)=I "sec"^(2)(phi)/(2)`
(`4I_(0)` is the intensity at the center of screen prior to intersectionof slit)
path difference `Deltax=(mu-1)t`
`(Deltax)/(lambda)=(Deltaphi)/(2pi) rArrphi=(2pi)/(lambda)Deltax rArr phi=(2pi)/(lambda)(mu-1)t`
`4I_(0)=Isec^(2)""(pi(mu-1)t)/(lambda)`
(b) path difference `=3lambda`
`(mu_(2)-mu_(1))t=3lambda`
`(1.7-1.4)t=3xx4xx10^(-7)`
`t=4xx10^(-6)m`
`t=4mum`