Accommodation: the increase in the eye's power that focuses near objects on the retina
Mechanism (Helmholtz)

The ciliary muscle contracts (parasympathetic, via the oculomotor nerve and ciliary ganglion)
The zonules relax, and the elastic capsule moulds the lens into a more rounded shape
The anterior lens surface steepens most (its radius falls from about 10 mm to about 5–6 mm); the lens thickens and moves slightly forward, and the anterior chamber shallows

## Far point, near point and range

Far point: the furthest point seen clearly with accommodation relaxed (see Ametropia)
Near point: the nearest point seen clearly with full accommodation
Range of accommodation: the distance between the far and near points
Amplitude of accommodation: the difference in dioptres between the far and near points

Amplitude = near point vergence − far point vergence, each as 1 ÷ distance in metres (points behind the eye negative)
Equivalently, for a fully corrected eye: amplitude = 1 ÷ near point distance (m)

Eye	Amplitude 4D: near point	Range
Emmetrope	1 ÷ 4 = 25 cm	Infinity to 25 cm
2D myope (far point 50 cm)	1 ÷ (2 + 4) = 16.7 cm	50 cm to 16.7 cm
2D hypermetrope	1 ÷ (4 − 2) = 50 cm	Only to 50 cm; 2D of the 4D is used up seeing in the distance

Measuring amplitude: the RAF rule (push-up to blur, through the distance correction), minus lenses to blur, or dynamic retinoscopy

## Age and presbyopia

Amplitude falls steadily from childhood because the lens nucleus hardens and the lens grows. Approximate values from Donders' classic table (values vary between studies)

Age 10: about 14D. Age 20: about 10D. Age 30: about 7D. Age 40: about 4.5D. Age 45: about 3.5D. Age 50: about 2.5D. Age 60 and over: about 1D or less, mostly depth of focus
Hofstetter's formulas: average amplitude = 18.5 − 0.3 × age; minimum = 15 − 0.25 × age

Presbyopia: the amplitude is too small for comfortable near work. It usually becomes symptomatic in the early to mid 40s, earlier in hypermetropes and later in myopes

Symptoms: holding reading matter further away ("arms too short"), blur and fatigue with near work, worse in dim light
Only about half the amplitude can be used comfortably for sustained work; the other half is held in reserve

## Calculating the near add

Working distance demand = 1 ÷ working distance (m). 40 cm needs 2.5D; 33 cm needs 3D

Worked example: a 50-year-old with an amplitude of 2D wants to read at 40 cm. Demand 2.5D; half the amplitude 1D. Add = 2.5 − 1 = +1.50D
Worked example: a 60-year-old with an amplitude of 1D reading at 33 cm. Add = 3 − 0.5 = +2.50D
The add is added to the distance prescription for each eye. Typical adds: about +1.00D at 45, +2.00D at 55, +2.50D by 60–65
Check the range through the add: with a +2.50D add and no accommodation, the clear point is 1 ÷ 2.5 = 40 cm. Too strong an add gives a working distance that is too close and a short range

An uncorrected myope of about −2.50D needs no add: reading distance is 40 cm, their far point
An uncorrected hypermetrope becomes symptomatic earlier, because part of the amplitude is spent on the distance error
Pseudophakic eyes have no true accommodation; they need a full add (about +2.50 to +3.00D) unless they have monovision or a multifocal or EDOF IOL

## Accommodation and convergence

AC/A ratio: accommodative convergence (in prism dioptres) per dioptre of accommodation. Normal is about 3–5Δ/D

Heterophoria method: AC/A = PD (cm) + (near deviation − distance deviation) ÷ near demand (D), with eso deviations positive
Gradient method: the change in deviation with a lens (e.g. −1.00D or +3.00D) ÷ the lens power. It excludes proximal convergence, so it gives a lower value
Worked example (gradient): at near, an esophoria of 10Δ becomes 4Δ through +2.00D lenses. AC/A = (10 − 4) ÷ 2 = 3Δ/D
Worked example (heterophoria): PD 6 cm, distance 2Δ eso, near (33 cm, 3D) 14Δ eso. AC/A = 6 + (14 − 2) ÷ 3 = 10Δ/D, a high ratio

A high AC/A causes convergence excess esotropia, worse for near. It is treated with bifocals or executive bifocals

Cycloplegia paralyses the ciliary muscle, abolishing accommodation. Used for cycloplegic refraction and to relieve ciliary spasm in uveitis
Accommodative spasm: excess accommodation gives pseudomyopia, with miosis and convergence. Retinoscopy shows a fluctuating myopic reflex that disappears with cycloplegia
Accommodative insufficiency: a lower amplitude than expected for age. Causes include Adie pupil, third nerve palsy, drugs (anticholinergics), diphtheria and botulism, and fatigue
Correcting presbyopia: reading glasses, bifocals, progressive lenses, monovision, multifocal or EDOF IOLs (see Prescribing Spectacles)