In YDSE 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 plane of slits and the screen is doubled. It is found that the distance between successive maxima (or minima) now is the same as the observed fringe shift upon the introduction of the mica sheet. Calculate the wavelength of the light.

Options

A. 3000 Å
B. 4850 Å
C. 5892 Å
D. None of these

Answer

C

Explanation

Clearly after removal of mica sheet, the new fringe width `(beta)` is
`beta.=((2D)lamda)/(d) ` . . . (i)
Initial fringe shift after the introduction of mica sheet is,
initial shift `=(D)/(d)(mu-1)t` . . (ii)
Equating (i) and (ii), `(2Dlamda)/(d)=(D)/(d)(mu-1)t`
`implies lamda=((mu-1)t)/(2)=((1*6-1)1*964xx10^(-6))/(2)=5892` Å