Optical system, image projection apparatus, and imaging apparatus

An optical system internally having an intermediate imaging position that is conjugated to a magnification conjugate point on a magnification side and a reduction conjugate point on a reduction side, respectively, the optical system comprising:

• a magnification optical system having a plurality of lens elements positioned on the magnification side with respect to the intermediate imaging position;
• a relay optical system having a plurality of lens elements positioned on the reduction side with respect to the intermediate imaging position;
• a spherical lens positioned first from the magnification side of the magnification optical system;
• a first aspherical lens arranged in the magnification optical system;
• a second aspherical lens arranged in the magnification optical system;
• and
• a third aspherical lens arranged in the relay optical system,
• wherein the magnification optical system includes:
• (i) a front group positioned on the magnification side with respect to an intersection position where a main ray of a furthest off-axis luminous flux is to intersect with an optical axis;
• and (ii) a rear group positioned on an intermediate imaging position side with respect to the intersection position,
• wherein the first aspherical lens is arranged in the front group,
• wherein the second aspherical lens is arranged in the rear group,
• wherein the optical system satisfies:
• 0.04<D1/LT<0.15;
• 0.04<D2/LT<0.15;
• and
• 0.01<D3/LT<0.07,
• wherein LT is a distance from a surface on the magnification side of the spherical lens to a surface on the reduction side of the lens element which is positioned first from the reduction side,
• wherein D1 is a distance from the surface on the magnification side of the spherical lens to a surface on the magnification side of the first aspherical lens,
• wherein D2 is a distance from the intermediate imaging position to a surface on the reduction side of the second aspherical lens, and
• wherein D3 is a distance from the intermediate imaging position to a surface on the magnification side of the third aspherical lens.