Physics - Wave Optics Question with Solution | TestHub

Position of nth dark fringes in Young’s double slit experiment is given,
$x_n=\frac{D}{d}\left(2n-1\right)\frac{\lambda }{2}$
$\Rightarrow \lambda =\frac{2x_{n}d}{D\left(2n-1\right)}$… (i)
Since, fifth dark fringe is formed opposite to one of the slit,
$\therefore 2x_5=d$(distance between slits)
Put$n=5$in Eq. (i), we get
$\lambda =\frac{2x_{5}d}{D\left(2\times 5-1\right)}$
$=\frac{d.d}{D\left(10-1\right)}\mathrm{}\left[\mathrm{s}\mathrm{i}\mathrm{n}ce,2x_5=d\right]$
$\frac{d^2}{9D}$