Question

In a young's doube slit experiment using mono-chromatic light, the fringe pattern shifts by a certain distance on the screen whwen a mica sheet of refractive index 1.6 and thickness 1.964 micron $(1micron={10}^{-6}m)$ is introduced in t epath of one of th einterfering 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 teh successive maxima now is the same as the observed fringe- shift upon th eintroduction of the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment.

Answer 1

In the given young's double slit experiment,
$\mu =1.6t=1.964Micron=1.964\times {10}^{-6}m$
We know, number of fringes shifted
$=\frac{(\mu -1)t}{\lambda }$
So, the corresponding shift $=No,offringesshifted\times fringewidth$
$=\frac{(\mu -1)}{\lambda }\times \frac{\lambda D}{d}=\frac{(\mu -1)tD}{d}$
Again when the distance between the screena nd the slits is doubled,
Fringe width = 1 (2d)
From (i) and (ii)
$\frac{(\mu -1)tD}{d}=\frac{\lambda \times 2D}{d}\Rightarrow \lambda =\frac{(\mu -1)t}{2}=\frac{(1.6-1)\times \left(1.964\right)\times {10}^{-6}}{2}=589.2\times {10}^I-9=589.2$