vertex

In optics, the vertex is the point on a lens surface closest to the optical axis, where that surface intersects the axis itself. For a spherical lens, it is the peak or pole of the curve. This single point determines where optical measurements begin: the radius of curvature, sag depth, and surface power are all calculated from the vertex as a reference.

Every lens has two vertices, one on each surface. The distance between them, measured along the optical axis, is the lens thickness. For a typical prescription eyeglass lens, the front surface vertex and rear surface vertex are separated by 2 to 4 millimeters depending on the lens design and material. In thick lenses or wide-aperture optical systems, the separation matters significantly for optical calculation.

Why vertex position matters

The vertex is the practical origin for many lens specifications. Back focal length, front focal length, and effective focal length are all measured from vertex positions. When a lens is mounted in a barrel or cell, the vertex often serves as the mechanical reference plane; manufacturing tolerances on vertex position directly affect image quality and proper focus. A vertex displacement of even 0.1 millimeter can shift focal length by a measurable amount in precision optical assemblies.

Measurement equipment such as lens gauges and optical benches locate the vertex first, then proceed from there. In digital imaging or microscopy, the working distance (space between lens front surface and specimen) is typically measured from the front vertex. Coated lenses, aspherical lenses, and Fresnel lenses all have vertices, though their positions may be defined mathematically rather than as a simple mechanical point.

The term comes from Latin, meaning the highest or turning point. In geometry it applies to any apex; in optics it retains that meaning: the geometrical peak of the lens surface where light enters or exits at its closest approach to the axis. Confusing the two vertices of a lens or misidentifying which surface is which is a common source of error in lens design and installation work.