In a Young's double slit experiment using monochromatic light, the fringe pattern shifts by as certasin distance on the screen when a mica sheet of refractive inde 1.6 and thickness 1.964 micron (1 micron `=10^-6m)` is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the screen and the slits is doubled. It is found that the distance between the successive maxima now is the same as the observed frige-shift upon the introduction of the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment.

Explanation

In the given Young's doule slit experiment
`mu=1.6`
t1.964micron
`=1.964xx10^-6m`
we know number of fringes shifted
`=((mu-1)t)/lamda`
so the corresponding shift=No. of fringes shifted xxfringe width
`=(mu-1)/lamdaxx(lamdaD)/d`
`=((mu-1)tD)/d.....i`
Again when the distance between the screen and the slits is doubled
fringe width `=1(2d)`..........ii
From i and ii
`((mu-1)tD)/d=(lamdaxx2D)/d`
`rarr lamda=((mu-1)t)/2`
`=((1.6-1)x(1.964)xx10^-6))/2`
`=589.2x10^-9=589.2m`