We present mock optical images, broad-band and H$alpha$ fluxes, and D4000 spectral indices for 30,145 galaxies from the EAGLE hydrodynamical simulation at redshift $z=0.1$, modelling dust with the SKIRT Monte Carlo radiative transfer code. The modelling includes a subgrid prescription for dusty star-forming regions, with both the subgrid obscuration of these regions and the fraction of metals in diffuse interstellar dust calibrated against far-infrared fluxes of local galaxies. The predicted optical colours as a function of stellar mass agree well with observation, with the SKIRT model showing marked improvement over a simple dust screen model. The orientation dependence of attenuation is weaker than observed because EAGLE galaxies are generally puffier than real galaxies, due to the pressure floor imposed on the interstellar medium. The mock H$alpha$ luminosity function agrees reasonably well with the data, and we quantify the extent to which dust obscuration affects observed H$alpha$ fluxes. The distribution of D4000 break values is bimodal, as observed. In the simulation, 20$%$ of galaxies deemed `passive for the SKIRT model, i.e. exhibiting D4000 $> 1.8$, are classified `active when ISM dust attenuation is not included. The fraction of galaxies with stellar mass greater than $10^{10}$ M$_odot$ that are deemed passive is slightly smaller than observed, which is due to low levels of residual star formation in these simulated galaxies. Colour images, fluxes and spectra of EAGLE galaxies are to be made available through the public EAGLE database.
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