An electronic device may include a display system and an optical system that are supported by a housing. The optical system may be a catadioptric optical system having first, second, and third lens elements. The first lens element may have a convex surface and a concave surface. The convex surface may have less curvature than the concave surface. An anti-reflective coating may be formed on the convex surface. A partially reflective mirror may be interposed between the first and second lens elements and a reflective polarizer may be interposed between the second and third lens elements. Alternatively, a partially reflective mirror may be interposed between the second and third lens elements and a reflective polarizer may be interposed between the first and second lens elements.