Fringe width \(\beta=\frac{\lambda D}{d}\)

Let \(n^{\text {th }}\) bright tringle of \(\lambda_1\) match with \(m ^{\text {th }}\) bright triangle of \(\lambda_2\)

\(\Rightarrow n \beta_1=m \beta_2\)

\(\Rightarrow n \lambda_1=m \lambda_2 \Rightarrow \frac{n}{m}=\frac{\lambda_2}{\lambda_1}=\frac{5500}{7000}\)

\(\Rightarrow \frac{n}{m}=\frac{11}{14}\)

Distance where bright fringe will match

\(=n \beta_1=\frac{11 \times 7000 \mathring A \times 150\, cm }{0.25\,cm }\)

\(=462 \times 10^{-5}\)