How is the focal length of a lens related to its curvature?

The correct answer highlights a fundamental principle in optics regarding lenses. The focal length of a lens is inversely proportional to its curvature, which can be understood through the lens maker's equation. This equation relates the focal length ( f ) of a lens to the radii of curvature of its two surfaces and the refractive index of the material.

As the curvature of the lens increases, meaning the lens becomes more sharply curved, the focal length decreases. This means that a lens with a greater curvature will bring light rays to a focus at a shorter distance compared to a lens with a shallower curvature. Therefore, when you have a lens that is more curved, it effectively bends the incoming light more sharply, resulting in a shorter focal length.

This relationship is crucial for designing lenses for specific optical applications, such as in cameras, glasses, and telescopes.

The other options suggest varying relationships that do not accurately reflect this fundamental optical principle. For instance, stating that the focal length is directly proportional to curvature would imply that increasing curvature also increases focal length, which contradicts the established understanding. Similarly, claiming that curvature has no effect or that focal length varies only with the lens material ignores the crucial role that curvature plays in determining how lenses focus light.