\(b \sin \theta=n \lambda \Rightarrow \sin \theta=\frac{n \lambda}{b}\)

Distance of \(\mathrm{n}^{\text {th }}\) secondary minima \(\mathrm{x}=\mathrm{D} \sin\, \theta\)

or \(\sin \theta_{1}=\frac{x_{1}}{D}\)

\(\sin \theta_{1}=\frac{2 \lambda}{b}\)

\(n=4\)

\(\sin \theta_{2}=\frac{4 \lambda}{b}=\frac{x_{2}}{D}\)

\(x_{2}-x_{1}=\frac{4 \lambda}{b}-\frac{2 \lambda}{b}=\frac{2 \lambda}{b}\)

\(3=\frac{2 \lambda}{b} \Rightarrow b=\frac{2 \lambda}{3}\)  ...... \((i)\)

Width of central maxima \(=\frac{2 \lambda}{b}\)

\(=\frac{2 \lambda}{\frac{2 \lambda}{3}}=3 \mathrm{cm}\)    ...  from eq. \((i)\)