What is the relationship between lens power and curvature?

The relationship between lens power and curvature is a fundamental concept in optics. Lens power is defined as the ability of a lens to converge (or diverge) light rays, and it is measured in diopters. The power of a lens is directly related to its curvature: a more curved lens has a greater optical power.

When the curvature of a lens increases, meaning the surfaces of the lens become more curved, the focal length of the lens decreases. This is due to the fact that a lens with a steeper curvature bends light more sharply, allowing it to focus light rays to a point much closer to the lens. Since lens power is inversely proportional to focal length (power = 1/focal length), a decrease in focal length results in an increase in lens power.

Therefore, as curvature increases, so does lens power, making this relationship a critical aspect to understand when working with corrective lenses and optical systems. Recognizing this connection is essential for those studying optics, vision correction, and lens design.