In Young's double slit experiment, using monochromatic light, fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thichness 1.964 mm is introduced in the path of one of the two waves. If now mica sheet is removed and distance between slit and screen is doubled, distance between successive max. or min. remains unchanged. The wavelength of the monochromatic light used in the experiment is

5892 Å

$\frac{xd}{D}=(u-1)t$ or $x=\frac{(u-1)tD}{d}$

when distance between screen and slit is doubled, them fringe width $∝=\frac{2λd}{d}$

As $∝=x$

$∴\frac{2λd}{d}=\frac{(u-1)tD}{d}$

or $λ=\frac{(u-1)t}{2}=\frac{(1.6-1)×1.96×10^{-6}}{2}$

$= 0.5892 ×10^{-6} m =5892 Å$