How a screw turns curvature into a measurement
A spherometer converts a shallow curve into a small, measurable height. Three outer legs touch the lens and establish a reference plane. The central screw is lowered until its tip meets the curved surface; its movement shows how far the lens rises or falls relative to that plane.
That height is called the sagitta. For a spherical surface, the sagitta and the distance between the central contact point and the outer legs determine the surface’s radius: the radius of the much larger sphere that the lens surface would belong to. A flatter surface has a smaller sagitta and a larger radius; a more strongly curved one has a larger sagitta and a smaller radius.
Why the three legs matter
The outer contacts make the instrument’s reference stable instead of relying on the lens’s edge, which may be uneven or shaped differently from the measured area. The screw’s calibrated movement supplies the height reading, while the known spacing of the contacts supplies the scale for the geometric calculation.
The result depends on measuring a surface that is close enough to spherical for that geometry to apply. On a lens with different curvature across its surface, readings at different spots can reveal that variation rather than describing the whole lens with one radius.
From surface shape to lens design
A lens bends light because its surfaces change direction as light passes through them. Knowing a surface’s radius helps describe that shape, which is essential when making or checking an optical surface. The spherometer does not measure how well the lens focuses by itself; it measures the curve that helps determine its optical behavior.
Its cleverness is in the scale of the measurement: a tiny screw movement records the shallow rise of the lens, and simple geometry turns that rise into the radius of a curve far larger than the instrument.
