How large something looks depends on the size of its retinal image, which depends on the visual angle it subtends (see Optics of the Eye)
Kinds of magnification

Lateral (linear) magnification: image size ÷ object size = v/u = U/V (see Spherical Lenses)
Angular magnification: the angle the image subtends with the device ÷ the angle the object subtends without it. Used for magnifiers and telescopes, where the image is at infinity
Axial magnification (along the axis) is the square of the lateral magnification. This is why depth is exaggerated through a high-power lens, e.g. in indirect ophthalmoscopy

## Relative distance and relative size magnification

Relative distance magnification: moving an object closer increases its visual angle

M = original distance ÷ new distance
Worked example: bringing print from 40 cm to 20 cm gives ×2. The reader then needs 5D of accommodation or a +5.00D add to focus at 20 cm

Relative size magnification: making the object bigger (large print). M = new size ÷ old size
Different kinds of magnification multiply: print twice as large, read at half the distance, gives ×4 (see low vision aids)

## Spectacle magnification

Spectacle magnification (SM): retinal image size in the corrected eye ÷ retinal image size in the same eye uncorrected
SM = power factor × shape factor

Power factor = 1 ÷ (1 − hF), where h is the distance from the lens to the entrance pupil in metres (about the vertex distance + 3 mm) and F is the back vertex power
Shape factor = 1 ÷ (1 − (t/n)F₁), from the front surface power F₁, thickness t and index n. It is close to 1 for thin lenses

Worked examples with h = 15 mm

+10.00D: 1 ÷ (1 − 0.15) = 1.18, so images are magnified by about 18%
−10.00D: 1 ÷ (1 + 0.15) = 0.87, so images are minified by about 13%

Plus lenses magnify and minus lenses minify. The effect grows with power and with distance from the eye, so it is least with contact lenses and least of all with IOLs

Correcting aphakia, approximate magnification compared with the phakic eye:

Aphakic spectacles (about +10 to +12D): 25–33%. Also pincushion distortion, a ring scotoma at the lens edge ("jack-in-the-box"), and diplopia if the other eye is phakic
Aphakic contact lens: about 7–10%
Posterior chamber IOL: about 1–3%

## Relative spectacle magnification and Knapp's law

Relative spectacle magnification (RSM): retinal image size in the corrected ametropic eye ÷ retinal image size in a standard emmetropic eye
Knapp's law: in axial ametropia, a correcting lens placed at the anterior focal point of the eye (about 15.7 mm in front of the cornea) gives an RSM of 1, the same image size as an emmetrope

Spectacles sit close to this point, so in axial anisometropia, spectacles keep the two retinal images similar in size
A contact lens in axial myopia gives a larger image than an emmetrope's, because it sits at the cornea rather than at the anterior focal point, so Knapp's law no longer applies

In refractive ametropia (the eye's length is normal but its power is not), contact lenses give an RSM close to 1, and spectacles do not
Practical rule: aniseikonia of about 1% per dioptre of anisometropia corrected with spectacles. Up to about 5% is usually tolerated (see anisometropia and aniseikonia)

In practice, axial anisometropes often tolerate contact lenses better than Knapp's law predicts, because a stretched myopic retina has more widely spaced photoreceptors, which offsets the larger image.

## Effect of lens position

Moving a lens further from the eye increases its effective power and moves the image forward, whether the lens is concave or convex (see effectivity in Spherical Lenses)

A sulcus-fixated IOL sits about 0.5–1 mm further forward than an IOL in the capsular bag. Further from the retina, it has a greater effective power, so a weaker IOL is chosen for the same refractive outcome: typically 0.5–1.0D less, depending on the IOL power.