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We have explored the capabilities of dust extinction and $\gamma$ rays toprobe the properties of the interstellar medium in the nearby anti-centreregion. We have jointly modelled the $\gamma$-ray intensity and the stellarreddening, E(B-V) as a combination of H$_{\rm I}$-bright, CO-bright, andionised gas components. The complementary information from dust reddening and$\gamma$ rays is used to reveal the dark gas not seen, or poorly traced, byH$_{\rm I}$, free-free, and $^{12}$CO emissions. We compare the total gascolumn densities, $N_{\rm{H}}$, derived from the $\gamma$ rays and stellarreddening with those inferred from a similar analysis (Remy et al. 2017) of$\gamma$ rays and of the optical depth of the thermal dust emission,$\tau_{353}$, at 353 GHz. We can therefore compare environmental variations inspecific dust reddening, E(B-V)/$N_{\rm H}$, and in dust emission opacity (dustoptical depth per gas nucleon), $\tau_{353}/N_{\rm{H}}$. Over the wholeanti-centre region, we find an average E(B-V)/$N_{\rm H}$ ratio of$(2.02\pm0.48)\times$ $10^{-22}$~mag~cm$^2$, with maximum local variations ofabout $\pm30\%$ at variance with the two to six fold coincident increase seenin emission opacity as the gas column density increases. In the diffuse medium,the small variations in specific reddening, E(B-V)/$N_{\rm H}$ implies a ratheruniform dust-to-gas mass ratio in the diffuse parts of the anti-centre clouds.The small amplitude of the E(B-V)/$N_{\rm H}$ variations with increasing$N_{\rm{H}}$ column density confirms that the large opacity$\tau_{353}/N_{\rm{H}}$ rise seen toward dense CO clouds is primarily due tochanges in dust emissivity. The environmental changes are qualitativelycompatible with model predictions based on mantle accretion on the grains andthe formation of grain aggregates.

Cosmic-rays, gas, and dust in nearby anti-centre clouds : III -- Dust extinction, emission, and grain properties