Optics and Spectacles

Optics and Spectacles is 2% of the COA exam, but the same ideas run through refractometry, lensometry, and contact lenses.

Refraction — light changes speed as it passes from one material into another, and it bends if it meets the boundary at an angle. A lens uses curved surfaces to bend light to a focus. Its power is measured in diopters, the reciprocal of the focal length in meters: a +2.00 D lens brings parallel light to a focus 50 cm away.

Lens basics — plus (convex, center-thick) lenses converge light and correct hyperopia; minus (concave, edge-thick) lenses diverge light and correct myopia; cylinders correct astigmatism along one meridian.

A cylinder has no power along its axis; its full power lies in the meridian 90° away.

Anisometropia — a large difference in prescription between the two eyes. Full correction in glasses can give the two eyes images of different sizes; contact lenses often handle a large difference better.

Reading an Rx — sphere / cylinder × axis, add for near, prism with base direction. Know OD (right), OS (left), OU (both) — and that a transposed Rx is the same prescription, not a different one.

Example — OD −2.00 −0.75 × 180, OS −1.50 DS, add +2.00 OU. DS (diopters sphere) means the left lens has no cylinder. The axis runs from 1 to 180 and is written with three digits (090, not 90).

Spherical equivalent — sphere plus half the cylinder: −2.00 −1.00 × 180 has a spherical equivalent of −2.50. It condenses a prescription to one number, for example as a starting point for a soft spherical contact lens.

Transposition — convert between plus- and minus-cylinder form: algebraically add sphere and cylinder, flip the cylinder sign, rotate the axis 90°.

To rotate the axis, add 90 to an axis of 90 or less and subtract 90 from an axis above 90, so the answer stays between 1 and 180.

The prism diopter — one prism diopter displaces light 1 cm at a distance of 1 m. Light bends toward the base, so the image appears shifted toward the apex. Base direction is named relative to the patient: base in (toward the nose), base out, base up, base down.

Prentice's rule — looking through a lens away from its optical center creates prism: prism diopters = decentration in centimeters × lens power in diopters. A −6.00 D lens decentered 3 mm (0.3 cm) induces 1.8 prism diopters.

Pupillary distance (PD) — the PD is measured so the optical centers sit in front of the pupils, where the lenses induce no prism. The near PD is a few millimeters smaller than the distance PD because the eyes converge to read. Faces are rarely symmetric, so each eye can be measured from the center of the nose (monocular PDs). The stronger the prescription, the less a centering error is forgiven.

Vertex distance — the spectacle plane sits ~12–14 mm from the cornea; above ±4.00 D, effective power changes meaningfully with vertex distance, and conversion matters when moving between spectacle and contact lens prescriptions.

Which way it changes — a minus lens gains effect as it moves closer to the eye and a plus lens loses effect. A high myope's contact lens therefore needs less minus than the glasses: −10.00 D glasses at 12 mm correspond to about −9.00 D at the cornea. A high hyperope's contact lens needs more plus. The same rule explains why sliding plus reading glasses down the nose makes them stronger.

Record it — any refraction above about ±4.00 D carries the vertex distance at which it was measured, so the lab and the contact lens fitter can convert it accurately.

Safety first — polycarbonate or Trivex is the standard recommendation for children, for anyone with only one seeing eye, and for sports and safety eyewear.

Coatings and tints — anti-reflective coating cuts reflections and glare; scratch-resistant coating protects plastic lenses; photochromic lenses darken in ultraviolet light. A tint is not UV protection: a dark lens that does not block UV opens the pupil and lets more UV in. Look for UV blocking to 400 nm.

Lens designs — single vision for one distance. Bifocals add a near segment, with its top usually set at the lower lid margin. Trifocals add an intermediate segment, set higher, at about the lower edge of the pupil. Progressive lenses change power gradually with no visible line; the fitting cross is set at the center of the pupil, and the lensometer reads the lens at its marked circles, not at a random spot.

Be ready to identify plus and minus lenses by shape and image movement, match each refractive error to its lens, read a prescription, find a spherical equivalent, transpose in both directions, define the prism diopter and name base directions, apply Prentice's rule, explain why vertex distance matters above ±4.00 D, and choose a lens material for a child or a strong prescription.