  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.
