The illumination optical apparatus of this invention is so arranged that light from a discharge lamp is collected by a rotationally symmetric collector mirror, the thus collected light is collimated into nearly parallel light by a collimator optical system, an optical integrator splits the parallel light into a plurality of light beams to form a plurality of secondary light sources, and thereafter the light from the secondary light sources is projected through a condenser optical system. A secondary light source distribution shaping portion is provided for shaping a light intensity distribution of the plural secondary light sources into a predetermined light intensity distribution, the two electrodes of the anode and cathode in the same discharge lamp are located in a predetermined relation, and an entrance surface of the optical integrator is located at a predetermined position with respect to a position where an image of a reflecting surface of the rotationally symmetric collector mirror is formed by the same collimator optical system.