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This is the first paper in a series that present a multi-wavelength analysisof the archetype Ultra-Luminous InfraRed Galaxy (ULIRG) IRAS FSC10214+4724, agravitationally lensed, starburst/AGN at z=2.3. Here we present a new lensmodel and spatially-resolved radio data, as well as a deep HST F160W map. Thelens modelling employs a Bayesian Markov Chain Monte Carlo algorithm withextended-source, forward ray-tracing. Using these high resolution HST, MERLINand VLA maps, the algorithm allows us to constrain the level of distortion tothe continuum spectral energy distribution resulting from emission componentswith differing magnification factors, due to their size and proximity to thecaustic. Our lens model finds the narrow line region (NLR), and by proxy theactive nucleus, is preferentially magnified. This supports previous claims thatpreferential magnification could mask the expected polycyclic aromatichydrocarbon spectral features in the Spitzer mid-infrared spectrum whichroughly trace the star-forming regions. Furthermore, we show thearc-to-counter-image flux ratio is not a good estimate of the magnification inthis system, despite its common use in the IRAS FSC10214+4724 literature. Ourlens modelling suggests magnifications of \mu ~ 15-20+-2 for the HST F814W,MERLIN 1.7 GHz and VLA 8 GHz maps, significantly lower than the canonicalvalues of \mu = 50-100 often used for this system. Systematic errors such asthe dark matter density slope and co-location of stellar and dark mattercentroids dominate the uncertainties in the lens model at the 40 percent level.

The preferentially magnified active nucleus in IRAS F10214+4724 - I. Lens model and spatially resolved radio emission