Question

In Young's double slit experiment the two slits are $d$ distance apart. Interference pattern is observed on a screen at a distance $D$ from the slits. A dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is :

• A. $\frac{D^2}{2d}$
• B. $\frac{d^2}{2D}$
• C. $\frac{D^2}{d}$
• D. $\frac{d^2}{D}$

Answer 1

The correct option is D $\frac{d^2}{D}$

The dark fringe is produced at a point just opposite to the slit $S_2$ i.e $y=\frac{d}{2}$

For dark fringe: $y=(2n-1)\frac{\lambda D}{2d}$ where $n=1,2,3,..........$

$\Rightarrow$$\frac{d}{2}=(2n-1)\frac{\lambda D}{2d}$

$\Rightarrow \lambda =\frac{d^2}{(2n-1)D}$

For $n=1$, $⟹$ $\lambda =\frac{d^2}{D}$