Explanation:
: We know that,
Band width \((\mathrm{B})=\frac{\lambda \mathrm{D}}{\mathrm{d}}\)
Position of \({ }^{\text {th }}\) bright fringe-
\(\mathrm{x}_{\mathrm{n}}=\frac{\mathrm{n} \lambda \mathrm{D}}{\mathrm{d}}=\mathrm{nB}\)
For, \(\mathrm{n}=1, \quad \mathrm{x}_1=\mathrm{B}\)
Position of \(n^{\text {th }}\) dark fringe-
\(x_n=\frac{(2 n-1) \lambda D}{2 d}=\frac{(2 n-1)}{2} B\)
For, \(\quad \mathrm{n}=1, \quad \mathrm{x}_1^{\prime}=\frac{\mathrm{B}}{2}\)
Required distance,
\(\mathrm{x}_1-\mathrm{x}_1{ }^{\prime}=\mathrm{B}-\frac{\mathrm{B}}{2}=\frac{\mathrm{B}}{2}\)
