\(\lambda=6000 \times 10^{-10}\, \mathrm{cm}=6 \times 10^{-7} \,\mathrm{cm}, \mathrm{D}=0.5\, \mathrm{m}\)

for \(3^{\text {rd }}\) dark band, \(a\,\sin \theta=3 \lambda\)

or \(\sin \theta=\frac{3 \lambda}{a}=\frac{x}{D}\)

The distance of the third dark band from the central bright band

\(x = \frac{{3\lambda D}}{a}\) \( = \frac{{3 \times 6 \times {{10}^{ - 7}} \times 0.5}}{{{{10}^{ - 4}}}}\) \(=\,9\,mm\)