The eye is a thick, compound lens system: the cornea and the crystalline lens separated by aqueous, with vitreous behind

Total power about +58 to +60D unaccommodated
Cornea about +43D (two thirds of the total). Most of it is at the air–tear interface, the largest change in refractive index
Lens about +19D unaccommodated, increasing with accommodation

Emmetropia: parallel light focuses on the retina with accommodation relaxed. The second principal focus (F′) lies on the retina

## The Gullstrand schematic eye

Gullstrand exact eye (unaccommodated)	Value
Total power	+58.64D (about +70.6D in full accommodation)
Cornea / lens power	+43.05D / +19.11D
Principal points P, P′	1.35 mm and 1.60 mm behind the cornea
Nodal points N, N′	7.08 mm and 7.33 mm behind the cornea
Anterior focal point F	15.7 mm in front of the cornea
Posterior focal point F′	24.4 mm behind the cornea

The principal points are close together, and so are the nodal points. Each pair can be merged into one with little error, which gives the reduced eye
The nodal points lie behind the principal points because the media in front (air) and behind (vitreous) differ

## The reduced eye

Treats the eye as a single refracting surface separating air from a medium of n = 1.336

Power +58.6D. Radius of curvature 5.73 mm
Principal point P 1.35 mm behind the cornea. Nodal point N 7.08 mm behind the cornea (at the centre of curvature of the surface)
Anterior focal length 17.05 mm (F lies 15.7 mm in front of the cornea). F′ lies 24.13 mm behind the cornea, 17.05 mm behind N

Nodal point: a ray directed at N passes through without deviation. This makes retinal image size easy to calculate
Limitations

The eye actually has several refracting surfaces and a lens of graded refractive index
Its surfaces are aspheric and its components are not perfectly aligned
It holds only for paraxial rays, so it ignores aberrations

Other reduced eyes use rounder numbers. Emsley's reduced eye has a power of +60D and n = 4/3, which is why the eye is often quoted as "+60D". Use whichever figures a question gives.

## Visual angle and retinal image size

The visual angle is the angle an object subtends at the nodal point
Retinal image size = object size × 17 mm ÷ object distance (both distances from N, in the same units)
Worked example: a 6/6 letter subtends 5 minutes of arc at 6 m, so it is 6000 × tan(5′) = 8.7 mm high. Its retinal image is 8.7 × 17 ÷ 6000 = 0.025 mm (about 25 µm)
Worked example: a 10 m tree 50 m away forms an image 10,000 × 17 ÷ 50,000 = 3.4 mm high
One minute of arc corresponds to about 5 µm on the retina, roughly the spacing of two foveal cones

Objects of different sizes at different distances that subtend the same visual angle form the same retinal image and look the same size. This is the basis of relative distance magnification (see Magnification)

## Pupil, depth of focus and the Stiles–Crawford effect

The entrance pupil is the image of the real pupil formed by the cornea: about 13% larger and about 0.5 mm in front of it. It is the pupil we see and measure
Depth of field (range of object distances in acceptable focus) and depth of focus (range of image positions) both increase as the pupil gets smaller
Stiles–Crawford effect (type I): light entering through the centre of the pupil stimulates cones more effectively than light entering near the edge, because cones are aligned towards the pupil centre and act as waveguides

It reduces the effect of spherical aberration and scattered light
Rods show little effect

## Axes and angles

Optical axis: the line through the centres of curvature of the cornea and lens
Visual axis: from the fixation point through the nodal points to the fovea
Pupillary axis: the line perpendicular to the cornea through the centre of the entrance pupil
Angle alpha: between the optical and visual axes, about 5°, because the fovea lies temporal to the optical axis
Angle kappa: between the visual and pupillary axes

Positive kappa (fovea temporal): the corneal reflex is displaced nasally, which mimics an exotropia
It is large in hypermetropia and when the macula is dragged temporally, e.g. in retinopathy of prematurity
Negative kappa mimics an esotropia. The cover test is unaffected

Night myopia (about 0.5–1D): spherical aberration through a large pupil, the shift of peak sensitivity towards blue in scotopic vision, and the resting (dark focus) state of accommodation
Instrument and empty-field myopia have a similar accommodative cause