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 another glass plate having the same thickness as the first one but having refractive index Interference pattern is observed using light of wavelength 5400A. It is observed that the point P on the screen where the central maximum (n=0) fell before the glass were inserted now has `3/4` th original intensity. It is further observed that what used to be the fifth maximum earlier, lies below the point P while the sixth minimum lies above P. Calculate the thickness of the glass plate.

Explanation

Path difference ` = (xd)/(D) + (n_2 - n_1) t`
For P, x = 0 , Path difference
` = (n^2 - n^1) t = 0.3t`
` I = I_0 cos^2 phi/2`
`(I)/(I_0) = cos^2 phi/2, cos phi/2 = (sqrt3)/(2)`
` phi/2 = phi/6 , phi = pi/3`
Path difference ` = (lamda)/(2 pi) phi = (lamda)/(2pi) pi/3 = pi/6`
` 0.3 t = 5 lamda + pi/6`