Schematic eye · paraxial ray trace
Change the length of the eye, the power of its cornea, the object it looks at, and the glasses in front of it — and watch where the light actually comes to a point.
What it is looking at
Measured from the spectacle plane, 14 mm in front of the cornea — the plane every prescription is referred to.
The eyeball
Emmetropic at 23.88 mm. Each extra millimetre costs about 2.7 D.
Normal cornea ≈ 43 D. A steep cornea makes a short eye myopic.
Accommodation
Spectacle lens · 14 mm vertex
No lens in the path.
The model. A two-surface schematic eye traced with paraxial vergences. Cornea 43 D at the vertex; the crystalline lens is a thin element of 20.82 D sitting 5.7 mm behind it, in a vitreous of n′ = 1.336. Together that is the textbook +60 D eye, which brings distant light to a point 23.88 mm behind the cornea — the axial length the sliders start at. Accommodation adds power to the crystalline lens alone, but is reported the way a clinician measures it: in dioptres at the spectacle plane, 14 mm in front of the cornea. Object distances are measured from that same plane, so 25 cm is a 4.00 D demand. The amplitude available follows Hofstetter's average, 18.5 − 0.3 × age, so it runs out around 60. Prescriptions are rounded to the nearest 0.25 D, the way a trial frame is.
Why the cornea and the lens don't simply add. Two lenses only add their powers when they sit in the same plane. The cornea and the crystalline lens are 5.7 mm apart, and light that has already been bent by the cornea arrives at the lens closer to the axis, where the lens can do less with it. The exact cost is d × Pcornea × Plens, with d the separation in metres divided by n′. For the default eye that is 43.0 + 20.8 − 3.8 = 60.0 D. Push the cornea and lens together and the loss vanishes; pull them apart and it grows, which is also why moving a spectacle lens toward or away from the eye changes the power it needs to be.
Focal length against eye length. The two readouts that matter most sit side by side. "Light converges at" is how far behind the front of the eye the rays come to a point — for a distant object, that is exactly the eye's focal length. "Length of the eye" is how far back the retina actually sits. Clear vision is those two numbers agreeing, and every refractive error here is them disagreeing: either the eye is the wrong length for its optics, or its optics are the wrong strength for its length.
The blur. The blur patch is the cone of light from a 4 mm pupil where the retina cuts across it, converted to visual angle at 0.288 mm per degree. "Sharp" means under 2 arcmin. Pupil size is fixed here, so nothing in the model changes it.
What the patient sees. The chart panel is drawn in visual angle, not in centimetres: each row is the letter size that defines its Snellen line, from a 50-arcmin E at 20/200 down to a 5-arcmin row at 20/20. It is then blurred by the same blur circle the ray trace produces, sampled as a uniform disc — which is what defocus actually does to an image, rather than the soft Gaussian most photo filters apply. The ≈ 20/x figure is a clinical rule of thumb fitted to the usual acuity-versus-defocus table, not a computed optical transfer function, so treat it as a line on a chart rather than a measurement.
What it leaves out. No astigmatism, no spherical or chromatic aberration, no diffraction, and a pupil fixed at 4 mm that never responds to light level or near effort, and a lens that changes power without changing its own principal planes. Object distance is drawn on a log scale so 15 cm and 6 m fit on one bench; the eye itself is to scale.