What characteristic of a lens affects both its focal length and image quality?

The characteristic of a lens that affects both its focal length and image quality is curvature. The curvature of a lens determines how light rays are refracted as they pass through it. Specifically, the degree of curvature influences the focal length of the lens; more curved surfaces generally result in shorter focal lengths, while less curved surfaces create longer focal lengths.

In addition to focal length, the curvature also plays a critical role in image quality. Lenses with improper curvature can lead to optical aberrations, which distort the image quality. For instance, spherical aberration arises when light rays entering the lens at different distances from the optical axis are focused at different points, resulting in a blur or reduced sharpness in the final image. Therefore, controlling the curvature is integral to both achieving the desired focal point and ensuring high image quality.

While other factors like material hardness, filtration, and thickness do have roles in lens design, they do not directly impact both focal length and image quality in the same way that curvature does. Material hardness affects durability and scratch resistance, filtration pertains to the wavelengths of light transmitted through the lens, and thickness can influence weight but is less critical in determining optical performance compared to curvature.