Optical system, image projection apparatus, and imaging apparatus

An optical system having a reduction conjugate point having a rectangular region on a reduction side and a magnification conjugate point having a rectangular region on a magnification side, and internally having an intermediate imaging position having a conjugate relationship with each of the reduction conjugate point and the magnification conjugate point, the optical system including:

• a prism provided on the magnification side, the prism formed of a transparent medium;
• and
• a sub-optical system provided between the reduction conjugate point and the prism, the sub-optical system including a plurality of optical elements and an aperture stop,
• wherein the prism includes a first transmission surface positioned on the reduction side, a second transmission surface positioned on the magnification side, and at least one reflection surface positioned on an optical path between the first transmission surface and the second transmission surface,
• wherein the aperture stop is positioned between the reduction conjugate point and the intermediate imaging position,
• wherein a first reflection surface closest to the first transmission surface on the optical path in the prism has a shape with a concave surface facing a direction into which a light ray made incident on the first reflection surface is reflected,
• wherein the second transmission surface has a shape with a convex surface facing the magnification side,
• wherein a part or the whole of an intermediate image formed at the intermediate imaging position is positioned inside a medium of the prism, and
• wherein the following Expression (1) or Expression (2) is satisfied:
• 0.4
• <
• (
• TN
• -
• (
• (
• NI
• -
• 1
• )
• /
• 8
• )
• )
• /
• PN
• 2
• <
• 0.64
• (
• 1
• )
• PN
• >
• 1.6
• (
• 2
• )
• where TN represents an average of d-line refractive indexes of positive lenses included in the sub-optical system, NI represents the number of intermediate images, and PN represents a line refractive index of the prism.