Optical system, image projection apparatus, and imaging apparatus

An optical system internally having an intermediate imaging position at which an intermediate image is formed, the intermediate imaging position being conjugate 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;
• and
• a relay optical system having a plurality of lens elements, positioned on the reduction side with respect to the intermediate imaging position,
• wherein a first lens element located closest to the magnification side among the plurality of lens elements in the magnification optical system is an aspherical lens having a negative power,
• the optical system simultaneously satisfies the following conditions (1) to (3):
• wherein the plurality of lens elements include a lens element that satisfies both of the conditions (6) and (7) and one lens element that does not satisfy both of the conditions (6) and (7):
• 0.0055<Δpgfn<0.030 (1)
• 53<vdn<58 (2)
• 0.28<fp/fr<1.0 (3)
• |ym/(fw·tan(ωm))|<3.0 (6)
• Tg>300° C. (7)
• where, Δpgfn=(ngn−nfn)/(nfn−ncn)−(−2.20599×10−3·vdn+6.69612×10−1), vdn is an Abbe number of the first lens element, ngn is a refractive index of the first lens element for a g-line, nfn is a refractive index of the first lens element for an F-line, non is a refractive index of the first lens element for a C-line, fp is a focal length of the magnification optical system, and fr is a focal length of the relay optical system at a wide-angle end,
• where, fw is a focal length of the entire optical system at the wide-angle end, om is a maximum half angle of view at the wide-angle end, ym is a height at the telephoto end at which the most off-axis main ray passes through a lens surface, and Tg is a glass transition point of lens material.