In YDSE experiment, the $4^{\text {th }}$ dark band is formed opposite to one of the slits. The wavelength…
In YDSE experiment, the $4^{\text {th }}$ dark band is formed opposite to one of the slits. The wavelength of light used is $(\mathrm{d}=$ distance between the slits, $\mathrm{D}=$ distance between source and the screen)
$\frac{d^2}{14 D}$
$\frac{d^2}{7 D}$
$\frac{\mathrm{d}^2}{9 \mathrm{D}}$
$\frac{d^2}{11 D}$
Solution
Distance of $4^{\text {th }}$ dark band from the centre $=3.5 \frac{\lambda \mathrm{D}}{\mathrm{d}}$
$\begin{aligned}
& \therefore \frac{d}{2}=\frac{3.5 \lambda D}{d} \\
& \therefore \lambda=\frac{d^2}{7 D}
\end{aligned}$
.