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Ophthalmic Optics

Light and Lens Theory

Light slows and bends (refracts) as it enters a denser medium, bending toward the normal. Convex (plus) surfaces converge light and produce a real focal point; concave (minus) surfaces diverge light and produce a virtual focal point.

Index of refraction n = speed of light in vacuum / speed in the material; higher n means thinner lenses.
Snell's law governs how much light bends at each surface.
Focal length (m) = 1 / power (D); power and focal length are reciprocals.

Lens Power and Vergence

Vergence is the convergence or divergence of light measured in diopters. For a thin lens, total power equals the algebraic sum of the front and back surface powers.

Thin-lens power = front surface power + back surface power.
A +2.00 D lens has a 50 cm focal length; a stronger plus lens focuses closer.
Surface power increases as radius of curvature decreases (steeper surface).

Sphere, Cylinder, Axis and Add

Sphere power corrects myopia or hyperopia, cylinder power corrects astigmatism at a specified axis (1 to 180 degrees), and the add is extra plus power for near vision in presbyopes.

Cylinder corrects astigmatism; the axis states its orientation.
The add is always a plus value added to the distance sphere for near.
Near power = distance sphere + add.

Prism and Prentice's Rule

A prism bends light toward its base and displaces the image toward its apex. Prism is measured in prism diopters, where one prism diopter deviates light 1 cm at 1 meter.

Prism (prism diopters) = decentration (cm) x lens power (D).
At the optical center there is no prismatic effect.
One prism diopter = 1 cm of displacement at 1 meter.

Lens Materials and Coatings

Materials vary in index, Abbe value (chromatic dispersion), weight, and impact resistance. CR-39 has a high Abbe value and low chromatic aberration; polycarbonate and Trivex are impact resistant.

Higher index yields thinner lenses but usually lower Abbe value and more color fringing.
Polycarbonate and Trivex are preferred for safety, sports, and children's eyewear.
AR coating reduces reflections; photochromics darken with UV; polarized filters cut horizontal glare.
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Last updated: July 2026

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