Physics - Wave Optics Question with Solution | TestHub

The position of the $n^{th}$ dark band from the central maximum is given by $y_n=(2n-1)\frac{\lambda D}{2d}$.

For the $4^{th}$ dark band, $n=4$.

$y_4=(2(4)-1)\frac{\lambda D}{2d}=\frac{7\lambda D}{2d}$

The point opposite to one of the slits is at a distance of $\frac{d}{2}$ from the central maximum.

Equating the two distances:

$\frac{7\lambda D}{2d}=\frac{d}{2}$

$7\lambda D=d^2$

$\lambda =\frac{d^2}{7D}$

Answer: $\frac{d^2}{7D}$