 Polychromatic single-slit diffraction

For mutually incoherent wavelengths, intensities add rather than amplitudes: $I(\theta )=\int S(\lambda ){\mathrm{sinc}}^2[\pi a\sin \theta /\lambda ]d\lambda$, where $\mathrm{sinc}q=\sin q/q$ and S includes source strength and detector response. All wavelengths share the central maximum but their minima occur at different angles. A smooth white spectrum therefore has a white centre, wavelength-dependent edge colours, no common first dark minimum and increasingly overlapped, low-contrast outer fringes. A particular hue needs the actual spectrum and colour response.