An optical system for image projection comprising: an illumination optical system (421a, 423a, 424a, 425a, 405, 406) which introduces a luminous flux emitted from a light source to an image-forming element through an optical surface having a light-splitting function; and a projection optical system which projects the luminous flux introduced from the image-forming element through the optical surface onto a projection surface, wherein the illumination optical system includes a conversion system (421a, 423a, 424a, 425a) which respectively converts the widths of the luminous flux in a first cross-section and in a second cross-section into widths different from those before entering thereinto, the first cross-section being parallel to a normal to the optical surface and a normal to an entrance surface of the image-forming element, and the second cross-section being perpendicular to the first cross-section, characterized in that, when a ratio obtained by dividing the outer diameter of the luminous flux at the exit of the conversion system by the outer diameter of the luminous flux at the entrance of the conversion system is defined as conversion rate, a first conversion rate of the width of the luminous flux by the conversion system in the first cross-section is smaller than a second conversion rate of the width of the luminous flux by the conversion system in the second cross-section, the conversion rates in the first and second cross-sections being not equal to 1, wherein the conversion system is a compression system which respectively compresses the widths of the luminous flux in the first and second cross-section, and the compression system includes, in order from a light source side, a first optical element having positive powers in the first cross-section and the second cross-section, a second optical element having negative powers in the first cross-section and the second cross-section, a third optical element having a negative power in the second cross-section, and a fourth optical element having a positive power in the second cross-section. an illumination optical system (421a, 423a, 424a, 425a, 405, 406) which introduces a luminous flux emitted from a light source to an image-forming element through an optical surface having a light-splitting function; and a projection optical system which projects the luminous flux introduced from the image-forming element through the optical surface onto a projection surface, wherein the illumination optical system includes a conversion system (421a, 423a, 424a, 425a) which respectively converts the widths of the luminous flux in a first cross-section and in a second cross-section into widths different from those before entering thereinto, the first cross-section being parallel to a normal to the optical surface and a normal to an entrance surface of the image-forming element, and the second cross-section being perpendicular to the first cross-section, characterized in that, when a ratio obtained by dividing the outer diameter of the luminous flux at the exit of the conversion system by the outer diameter of the luminous flux at the entrance of the conversion system is defined as conversion rate, a first conversion rate of the width of the luminous flux by the conversion system in the first cross-section is smaller than a second conversion rate of the width of the luminous flux by the conversion system in the second cross-section, the conversion rates in the first and second cross-sections being not equal to 1, wherein the conversion system is a compression system which respectively compresses the widths of the luminous flux in the first and second cross-section, and the compression system includes, in order from a light source side, a first optical element having positive powers in the first cross-section and the second cross-section, a second optical element having negative powers in the first cross-section and the second cross-section, a third optical element having a negative power in the second cross-section, and a fourth optical element having a positive power in the second cross-section.