A spectacle lens alters retinal image size in two ways: its power and how far it sits from the eye (power factor), and its front curve, thickness and index (shape factor). When the two eyes see different image sizes, that is aniseikonia. Knapp’s law promises normal image size for axial errors, yet in real eyes it often falls short.
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What spectacle magnification is
Spectacle magnification compares the image size an eye gets through its glasses with the size it gets uncorrected. It has two parts, covered below. Brooks and Borish write it as the shape factor times the power factor; the Iowa optics review adds the two as percentages for a quick estimate.
Power factor: power and vertex distance
This part depends on the back vertex power and the lens-to-eye distance. Push plus power farther out and it magnifies more; push a minus lens farther out and it shrinks the image more. Bring either closer and the effect eases. Try distances in the vertex distance calculator, and see vertex distance.
Shape factor: front curve, thickness, index
The shape part is set by front surface power, center thickness and index, the parts of the lens that act like a tiny telescope with no net power. A steeper front or a thicker lens increases it. Related: base curve and lens power, lens thickness and sagitta.
Aniseikonia
Aniseikonia means each eye perceives an image of a different size or shape. It matters most when the two prescriptions differ a lot, because each lens then magnifies by a different amount.
Knapp's law, and where it breaks down
Put simply, by Knapp’s law, for ametropia caused by eye length, a lens positioned at the front focal point restores a normal-size retinal image. Reality is messier. The Iowa optics review points out that eye length is seldom the sole cause of a refractive error, and a long myopic eye has a stretched retina, so the image the brain gets isn’t the size the theory predicts.
Original practice set
Original problems.
Two plus lenses have equal power and thickness. One has a steeper front curve. Which magnifies more?
Show answer
The steeper one (larger shape factor).
A minus wearer lets the frame slip down so the lenses sit farther out. What happens to image size?
Show answer
Images get smaller; minification increases.
A plano sunglass lens with a strong front curve and some thickness. Any magnification?
Show answer
Yes, a little, from the shape factor, even with no net power.
Name the two parts of spectacle magnification.
Show answer
The power factor and the shape factor.
Knapp’s law assumes what kind of ametropia?
Show answer
Axial (due to eye length).
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Frequently asked questions
What is spectacle magnification?
The change in retinal image size a spectacle lens causes, compared with the same eye seeing without it. It has two parts, a power factor and a shape factor. Brooks and Borish combine them by multiplying; the Iowa optics review uses a simpler shortcut that adds the two as percentages.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
What is the difference between the shape factor and the power factor?
The power factor is set by lens power and its distance from the eye. The shape factor depends on the front curve, center thickness and refractive index, and applies even to a lens with no net power.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
Does a steeper base curve make a lens magnify more?
Yes. A steeper front curve raises shape magnification, and so does a thicker lens.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
Why do minus lenses make things look smaller?
Through the power factor, a minus lens minifies, and the effect grows as the lens moves farther away. Plus power does the opposite and magnifies more when moved out.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
What is aniseikonia?
A mismatch in image size or shape between one eye and its partner.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
What does Knapp's law say?
In paraphrase: if an eye’s ametropia comes from its length, a correcting lens positioned at the front focal point gives a retinal image the same size as an emmetropic eye’s.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
Why doesn't Knapp's law always work in practice?
The Iowa optics review notes that eye length is seldom the sole cause of a refractive error. Both it and Brooks and Borish also point out that in a long myopic eye the retina is stretched, so the effective image size isn’t what theory predicts.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
Official sources
- Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 21 Anisometropia, pp. 491, 493–494, 496–498 (opens in a new tab)
- University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), §23 Knapp’s Law p. 50; §29 pp. 74, 77 (opens in a new tab)
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