In Young's double slit experiment the two slits are 'd' distance apart. Interference pattern is observed on…
In Young's double slit experiment the two slits are 'd' distance apart. Interference pattern is observed on a screen at a distance ' $\mathrm{D}$ ' from the slits The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is
$\frac{\mathrm{D}^2}{2 \mathrm{~d}}$
$\frac{\mathrm{D}^2}{\mathrm{~d}}$
$\frac{\mathrm{d}^2}{2 \mathrm{D}}$
$\frac{\mathrm{d}^2}{\mathrm{D}}$
Solution
The dark fringe is produced at a point just opposite to the slit, i.e., $y=\frac{d}{2}$
For dark fringe: $\mathrm{y}=(2 \mathrm{n}-1) \frac{\lambda \mathrm{D}}{2 \mathrm{~d}}$ where, $\mathrm{n}=1,2,3, \ldots \ldots .$. is the order of the fringe.
$\begin{aligned} & \Rightarrow \frac{d}{2}=(2 n-1) \frac{\lambda D}{2 d} \\ & \Rightarrow \lambda=\frac{d^2}{(2 n-1) D}\end{aligned}$
For $\mathrm{n}=1, \lambda=\frac{\mathrm{d}^2}{\mathrm{D}}$