We study the near-infrared (NIR) scattering in LDN 1642, its correlation with the cloud structure, and the ability of dust models to simultaneously explain sub-millimetre emission, NIR extinction, and NIR scattering. We use observations from the HAWK-I instrument to measure the NIR surface brightness and extinction. These are compared with Herschel data on dust emission and, with radiative transfer modelling, with predictions calculated for different dust models. We find an optical depth ratio $tau(250,mu{rm m})/tau(J)approx 10^{-3}$, confirming earlier findings of high sub-millimetre emissivity. The relationships between the column density derived from dust emission and the NIR colour excesses is linear and consistent with the standard NIR extinction curve. The extinction peaks at $A_J=2.6,$mag, the NIR surface brightness remaining correlated with $N({rm H}_2)$ without saturation. Radiative transfer models can fit the sub-millimetre data with any of the tested dust models. However, these predict a NIR extinction that is higher and a NIR surface brightness that is lower than in observations. If the dust sub-millimetre emissivity is rescaled to the observed value of $tau(250,mu{rm m})/tau(J)$, dust models with high NIR albedo can reach the observed level of NIR surface brightness. The NIR extinction of the models tends to be higher than directly measured, which is reflected in the shape of the NIR surface brightness spectra. The combination of emission, extinction, and scattering measurements provides strong constraints on dust models. The observations of LDN 1642 indicate clear dust evolution, including a strong increase in the sub-millimetre emissivity, not yet fully explained by the current dust models.
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