Observations in the submillimetre (submm) waveband have recently revealed a
new population of luminous sources. These are proposed to lie at high reds
hift and to be optically faint because of their high intrinsic dust obscura
tion. The presence of dust has been previously invoked in optical galaxy co
unt models which use the Bruzual & Chariot evolution models with an exponen
tial tau = 9 Gyr star formation rate (SFR) for spirals, and these fit the c
ount data well from U to K. We now show that by using either a 1/lambda or
Calzetti absorption law for the dust and re-distributing the evolved spiral
galaxy ultraviolet (UV) radiation into the far-infrared (FIR), these model
s can account for all of the 'faint' (less than or equal to1 mJy) 850-mum g
alaxy counts, but fail to fit 'bright' (greater than or equal to2 mJy) sour
ces, indicating that another explanation for the submm counts may apply at
brighter fluxes, e.g., quasi-stellar objects (QSOs) or ultraluminous infrar
ed galaxies (ULIRGs). We find that the main contribution to the faint, subm
m number counts is in the redshift range 0.5 < z < 3, peaking at z = 1.8. T
he above model, using either dust law, can also explain a significant propo
rtion of the extragalactic background at 850 mum, as well as producing a re
asonable fit to the bright 60-mum IRAS counts.