= Solution
The two <wavelengths> have independent <interference> patterns. Their <interference fringe> spacings are
$$
\boxed{\beta_g=\frac{546\times10^{-9}\times0.5}{100\times10^{-6}}=2.730\,\mathrm{mm},\qquad
\beta_b=\frac{437\times10^{-9}\times0.5}{100\times10^{-6}}=2.185\,\mathrm{mm}.}
$$
Different optical <frequencies> do not maintain a fixed mutual <phase> over the detector's integration time, so their <intensities> add. For narrow equal slits, suppressing the slowly varying <diffraction> envelopes, one may write
$$
I(y)=I_{g,\max}\cos^2\!\left(\frac{\pi y}{\beta_g}\right)+I_{b,\max}\cos^2\!\left(\frac{\pi y}{\beta_b}\right).
$$
The relative line strengths are not supplied; the figure illustrates equal peak <intensities> rather than inferring a quantitative brightness ratio. At $y=0$ both colours are bright, producing a blue-green mixture. Away from the centre the green and blue <interference fringes> progressively separate, creating alternating colour and brightness variations; places where one line is dark can still be bright in the other. Neither two-line mixing nor its central maximum is generally white.
Across $-15\,\mathrm{mm}\leq y\leq15\,\mathrm{mm}$, the green maxima occur at $y=2.730m\,\mathrm{mm}$ for $m=-5,\ldots,5$, and the blue maxima at $y=2.185n\,\mathrm{mm}$ for $n=-6,\ldots,6$. Near $y=\pm10.92\,\mathrm{mm}$, the fourth green and fifth blue maxima nearly coincide: $4\beta_g=10.920\,\mathrm{mm}$ and $5\beta_b=10.925\,\mathrm{mm}$. The $5\,\mu\mathrm m$ mismatch shows that these are near coincidences, not exact ones for the given <wavelengths>. The plotted central interval includes all these maxima.
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