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Excerpt from Field Guide to Visual and Ophthalmic Optics

Vergence is a concept in ophthalmic optics in which distances are converted to a dioptric power. Vergence is defined as

Vergence Equation

where d is the absolute distance between an object and a plane of interest, and n is the refractive index of the space. By convention, converging light has a positive vergence and diverging light has a negative vergence. Zero vergence occurs when the object is at infinity. Vergence is in units of diopters for d in meters.


Based on vergence, the lens formula is

Lens Formula

where U is the object vergence, φ is power of the lens, and V is image vergence. For a thin lens, the plane of interest for both vergences is at the lens. For thick lenses, the planes of interest are the front and rear principal planes. The magnification is U / V.

Object Vergence (D)Distance
–0.254 m
–0.502 m
–1.001 m
–2.0050 cm
–3.0033 cm
–4.0025 cm
–5.0020 cm
–6.0016.6 cm
–7.0014.2 cm
–8.0012.5 cm
–9.0011.1 cm
–10.0010 cm

J. Schwiegerling, Field Guide to Visual and Ophthalmic Optics, SPIE Press, Bellingham, WA (2004).

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