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EX Hya is one of the few double-lined eclipsing cataclysmic variables thatallow an accurate measurement of the binary masses. We analyze orbitalphase-resolved UVES/ VLT high resolution spectroscopic observations of EX Hyawith the aims of deriving the binary masses and obtaining a tomographic imageof the illuminated secondary star. We present a novel method for determiningthe binary parameters by directly fitting an emission model of the illuminatedsecondary star to the phase-resolved line profiles of NaI lambda 8183/ 8195 inabsorption and emission and CaII lambda 8498 in emission. The fit to the NaIand CaII line profiles, combined with the published K1, yields a white-dwarfmass M1 = 0.790 +/- 0.026 Msun, a secondary mass M2 = 0.108 +/- 0.008 Msun, anda velocity amplitude of the secondary star K2 = 432.4 +/- 4.8 km s-1. Thesecondary is of spectral type dM5.5 +/- 0.5 and has an absolute K-bandmagnitude of MK = 8.8. Its Roche radius places it on or very close to the mainsequence of low-mass stars. It differs from a main sequence star by itsilluminated hemisphere that faces the white dwarf. The secondary starcontributes only 5% to the observed spin-phase averaged flux at 7500 A, 7.5% at8200 A, and 37% in the K-band. We present images of the secondary star in thelight of the NaI doublet and the CaII emission line derived with a simplifiedversion of Roche tomography. We have discovered narrow spectral lines from thesecondary star in EX Hya that delineate its orbital motion and allow us toderive accurate masses of both components. The primary mass significantlyexceeds recently published values. The secondary is a low-mass main sequencestar that displays a rich emission line spectrum on its illuminated side, butlacks chromospheric emission on its dark side.

High-resolution spectroscopy of the intermediate polar EX Hydrae. I. Kinematic study and Roche tomography