Question

In Young's double slit experiment the two slits are $0.6mm$ distance apart. Interference pattern is observed on a screen at a distance $80cm$ from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be _______ $nm.$

Answer 1

As first dark fringe is in opposite of slit so,
$y=\frac{d}{2},$
Also, we know that,
$\therefore \Delta x=y\frac{d}{D}$
$\Rightarrow \frac{d^2}{2D}=\frac{\lambda }{2}$
$\Rightarrow \lambda =\frac{{(0.6\times {10}^{-3})}^2}{0.8}$
$=450nm$