At a point on the two-slit interference pattern obtained using a … - Vidyadip

Question

At a point on the two$-$slit interference pattern obtained using a source of green light of wavelength $5500 A$, the path difference is $4.125\ pm$. Is the point at the centre of a bright or dark fringe? Hence, find the order of the fringe.

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Answer

Path difference, $\Delta I=4.125 \times 10^6 \lambda=5500 A =5.5 \times 10^7 m$
Let $p$ be an integer such that $p_2 \frac{i}{2}-\Delta l$,
$\therefore \mu=\frac{2 \Delta l}{\lambda}=\frac{2 \times 4.125 \times 10^{-4}}{5.5 \times 10^{-7}}-\frac{8.25 \times 10}{5.5}$
$-\frac{k 25}{55}-15$
$\therefore \Delta l=15 \frac{\lambda}{2}$
As the path difference is an odd integral multiple of $\frac{\lambda}{2}$ the point is at the centre of a dark fringe.
$\therefore p=2 m-1(m=1,2,3 \ldots)$
$\therefore 2 m-1=15$
$\therefore m=8$
$\therefore$ The order of the fringe is $8 ($i.e, the point lies at the centre of the $8$ th dark fringe$).$

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