Clinical Optics Made Easy: Vergence, Prisms and Magnification

Last updated: October 2026

Optics frightens residents because it is taught as a page of formulas. In practice almost every clinical optics question comes back to a handful of ideas: vergence, the far point, prisms, accommodation and magnification. Learn these and the formulas become common sense.

Five ideas

Numbers worth knowing

Effective power and vertex distance

When a lens moves towards the eye by d metres, its new power is F ÷ (1 − dF). If it moves away, use + d. It matters above about ±4 D: a −10.00 D spectacle lens at 12 mm becomes about −8.90 D at the cornea, so the contact lens is weaker for a myope and stronger for a hyperope.

Memory hook: Contact lens for a myope: minus less. Contact lens for a hyperope: higher plus.

Astigmatism in three sentences

• A cylinder has no power along its axis and full power at 90° to it. Light through an astigmatic system forms two focal lines (the conoid of Sturm) with the circle of least confusion at the spherical equivalent.
• With-the-rule: the vertical meridian is steepest (plus cyl at 90 or minus cyl at 180), common in the young. Against-the-rule is common in older people.
• Transposition: add the cylinder to the sphere, change the cylinder's sign, rotate the axis by 90°. −1.00/+2.00 × 90 = +1.00/−2.00 × 180.

Memory hook: The plus-cylinder axis lies along the steep meridian. Jackson cross-cylinder: refine the axis first, then the power; keep the spherical equivalent constant by changing the sphere half as much in the opposite direction.

Accommodation by age

Approximate averages; published tables (Donders, Duane) differ by a dioptre or so.

Worked example: a 50-year-old emmetrope (amplitude 2.5 D) wants to read at 40 cm (demand 2.5 D). Keep half (1.25 D) in reserve, so the add is 2.5 − 1.25 = +1.25 D. A higher add brings the reading distance closer and narrows the range.

Prisms in practice

• Prentice's rule: 5 mm decentration of a +6 D lens gives 0.5 × 6 = 3 Δ.
• Base direction for a decentred lens: plus lenses act like two prisms base to base, so decentring a plus lens in gives base-in prism; minus lenses give the opposite.
• Correcting a deviation: the apex points the way the eye turns: esotropia → base-out, exotropia → base-in, right hypertropia → base-down over the right eye.
• Vertical imbalance in anisometropic bifocal wearers when reading: fix with slab-off (bicentric grinding) on the more minus lens.

Magnification and aniseikonia

• Knapp's law: in axial ametropia, a spectacle lens at the anterior focal point of the eye (about 15 mm) gives a retinal image the same size as an emmetrope's. So axial anisometropia tolerates glasses; refractive anisometropia (aphakia, post-keratoplasty) does better with contact lenses.
• Most people tolerate about 5% aniseikonia (roughly 2–3 D of spectacle anisometropia).
• Low vision: magnification needed = target acuity ÷ current acuity, as decimals (from 6/60 to 6/12 is 0.5 ÷ 0.1 = 5×). A +20 D magnifier gives 5×.
• Telescopes: M = − eyepiece power ÷ objective power. Galilean (plus objective, minus eyepiece) is short with an upright image; Keplerian (two plus lenses) is longer and needs a prism to turn the image upright.

Purkinje images

Test yourself: flip cards

Quick quiz

Related: Optics lectures, Spectacle transposition tool, Spectacle dispensing reference, Low vision aids calculator, ICO optics mock test.

Key sources

• American Academy of Ophthalmology. Basic and Clinical Science Course, Section 3: Clinical Optics and Vision Rehabilitation (current edition)
• Elkington AR, Frank HJ, Greaney MJ. Clinical Optics, 3rd ed. Blackwell Science; 1999
• Duane A. Studies in monocular and binocular accommodation with their clinical applications. Am J Ophthalmol. 1922;5:865-877