Past exam of the physics 2 paper of the University of Oxford / 2019 / 11 / c

The two wavelengths have independent interference patterns. Their interference fringe spacings areDifferent 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 writeThe 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 $-15\mathrm{mm}\le y\le 15\mathrm{mm}$, the green maxima occur at $y=2.730m\mathrm{mm}$ for $m=-5,\dots ,5$, and the blue maxima at $y=2.185n\mathrm{mm}$ for $n=-6,\dots ,6$. Near $y=\pm 10.92\mathrm{mm}$, 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.