The fringe width in an interference pattern is ' $X$ '. The distance between the sixth dark fringe from one…
The fringe width in an interference pattern is ' $X$ '. The distance between the sixth dark fringe from one side of central bright band to the fourth bright fringe on other side is
1.5 X
2 X
5.5 X
9.5 X
Solution
Fringe width is given by, $W=\frac{\lambda D}{d}=X$
...(given)
Position of $4^{\text {th }}$ bright fringe $=n \frac{\lambda D}{d}=4 X$
$\begin{aligned}
\text { Position of } 6^{\text {th }} \text { dark fringe } & =(2 \mathrm{n}-1) \frac{\lambda \mathrm{D}}{2 \mathrm{~d}} \\
& =(2(6)-1) \frac{\mathrm{X}}{2} \\
& =5.5 \mathrm{X}
\end{aligned}$
$\therefore \quad$ Total distance $=(4+5.5) \mathrm{X}=9.5 \mathrm{X}$