b
For common maxima, \(n_{1} \lambda_{1}=n_{2} \lambda_{2}\)

\(\Rightarrow \quad \frac{n_{1}}{n_{2}}=\frac{\lambda_{2}}{\lambda_{1}}=\frac{520 \times 10^{-9}}{650 \times 10^{-9}}=\frac{4}{5}\)

For \(\lambda_{1}\)

\(y=\frac{n_{1} \lambda_{1} D}{d}, \lambda_{1}=650\, \mathrm{nm}\)

\(y=\frac{4 \times 650 \times 10^{-9} \times 1.5}{0.5 \times 10^{-3}} \quad\) or, \(y=7.8\,\mathrm{mn}\)