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  4. In young’s Double Slit Experiment, the distance between the slits and the screen is 1.2 m and the distance between the two slits is 2.4 mm. If a thin transparent mica sheet of thickness 1 μ m and R.I. 1.5 is introduced between one of the interfering beams, the shift in the position of central bright fringe is

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Q. In young’s Double Slit Experiment, the distance between the slits and the screen is 1.2 m and the distance between the two slits is 2.4 mm. If a thin transparent mica sheet of thickness $1 \mu m$ and R.I. 1.5 is introduced between one of the interfering beams, the shift in the position of central bright fringe is

KCETKCET 2020Wave Optics

Solution:

Path difference due to insertion of mica sheet $\Delta x =(\mu-1) t$
Let the shift in the fringe pattern be $'y'$
Also, path difference $\Delta x=y \times d / D$,
so comparing both $(\mu-1) t=y \times(d / D)$
$y =(\mu-1) t \times( D / d )$,
where $\mu=1.5, D =2.4$ and $d =1.2$
putting the values, we get
$y =0.25 \,mm$.