In a Young's double slit experiment using monochromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 microns is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the slits and screen is doubled. It is found that the distance between successive maxima now is the same as observed fringe shift upon the introduced of the mica sheet . Calculate the wavelength of the monochromatic light used in the experiment .

Answer

`5892 Å`

Explanation

Shift, `y_(0) = (beta)/(lambda)(mu - 1)t`
`= (beta)/(lambda)(16.1 - 1) xx 1.964 xx 10^(-6)m`
`= (1.1784 xx 10^(-6)beta)/(lambda)`
Distance between successive maxima
`beta = (lambda D)/(d)`, i.e., `beta prop D`
As `D` is doubled, `beta` becomes twice.
As per question, `y_(0) = 2 beta = (beta)/(lambda) xx 1.1784 xx 10^(-6)`
`lambda = (1.1784 xx 10^(-6))/(2)m = 0.5892 xx 10^(-6)m = 5892 Å`