The geometry of a two dimensional, digital, electro-optic light deflector is discussed. The deflector consists of a light modulator, stages for horizontal and vertical deflection, the polarization confirmator and the condensing lens. A modulator does not pass the light during the time of switching. A polarization confirmator eliminates the parasitic light of the first order. Each stage contains a polarization switch based on a transverse field Pockels effect and an isosceles prism of calcite. Each switch consists of two identical plates of KD*P separated by a suitably oriented half-wave plate. As far as the disposition of deflection stages is concerned, one can either group together the p stages of horizontal deflection and then the p stages of vertical deflection or these can be placed alternately; in addition the 2 p stages can either be placed in the same box or in two boxes separated by an afocal system. These four possibilities are discussed with the aim that the deflectors comprising a large number of switch stages should have reasonable dimensions (none of the dimensions should exceed 2 cm). It is shown, that it is possible to construct a deflector of 210 X 210 positions, resolved according to Rayleigh's criterion, with switching voltage of 0.9 kV on 14 stages and 2 kV on the last six. The stages of horizontal and vertical deflections are alternated and are placed in two boxes; the first contains 14 stages and the second 6. The bisecting planes of last prism in each of the boxes are conjugated with the help of a telecentric lens system of 1.45 magnification. The experimental realization of a deflector of 27 X 27 completely resolved positions is described. The stages of horizontal deflection and of vertical deflection are grouped together and are placed in two boxes. The telecentric lens system works at unity magnification. The switching voltage requires 1.1 kV on the stages of horizontal deflection and 1.8 kV on the stages of vertical deflection. We obtain 105 positions per second for random access. The total loss of light is of the order of 3 dB, provided the optical surfaces are suitably coated. Adressing due to spurious intensity is about 1% per stage without polarization confirmator; this latter reduces the parasitic light to about 0.1%.