Optical Theory and Principles
Vergence and imaging
Vergence is 1/f measured in meters, expressed in diopters. Snell's law, n1 sin theta1 = n2 sin theta2, governs refraction at every surface. Surface power follows F = (n lens minus n surround) divided by radius of curvature, and thin lenses in contact simply add powers. The eye's total power of about 60 D is mostly cornea (about 43 D) plus crystalline lens (about 20 D).
Astigmatism and transposition
Cylinder power exists only in one meridian; the axis is the meridian of zero cylinder power. Spherical equivalent equals sphere plus one-half the cylinder, and it describes the power of the circle of least confusion.
Prentice rule
Induced prism P = c times F, where c is decentration in centimeters. The base always lies at the thickest part of the lens: toward the optical center for a plus lens, toward the edge for a minus lens.
Vertex distance
F new = F divided by (1 minus d times F), with d in meters and positive when the lens moves away from the eye. Plus lenses gain effective power as they move away; minus lenses lose power.
Aberrations and limits
Spherical aberration, chromatic aberration (tied to Abbe value), coma, oblique astigmatism, and distortion. Base curve selection minimizes oblique astigmatism, and spectacle magnification depends on power, thickness, vertex distance, and base curve.
Worked example
A +10.00 D lens is worn at 12 mm and the frame is refit at 14 mm. Here d times F is 0.002 times 10, or 0.02, so the new power is 10 divided by 0.98, which equals +10.20 D, dispensed as +10.25 D. Trap: applying the correction in the wrong direction or forgetting that only higher powers show a meaningful change.