We present a pilot study of atmospheres of accreting magnetic white dwarfs irradiated by intense fluxes at ultraviolet to infrared wavelengths. The model uses a standard LTE stellar atmosphere code which is expanded by introducing an angle-dependent external radiation source. The present results are obtained for an external source with the spectral shape of a 10 000 K blackbody and a freely adjustable spectral flux. The model provides an explanation for the observed largely filled-up Lyman lines in the prototype polar AM Herculis during its high states. It also confirms the hypotheses (i) that irradiation by cyclotron radiation and other radiation sources is the principle cause for the large heated polar caps surrounding the accretion spots on white dwarfs in polars and (ii) that much of the reprocessed light appears in the far ultraviolet and not in the soft X-ray regime as suggested in the original simple theories. We also briefly discuss the role played by hard X-rays in heating the polar cap.\u
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