# Eye Optics Simulator - Myopia, Astigmatism, Glasses & Rx Reader

> Reduced-eye ray diagrams for myopia, hyperopia, astigmatism and presbyopia, a blurred eye chart, far/near points, glasses vs contacts power, Rx reader.

- URL: https://qilingtools.com/en/physics/eye
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

An educational simulator based on the Emsley reduced eye (one refracting surface of about 60 D and an axial length of about 22.2 mm). Adjust sphere, cylinder and axis, age (accommodation), pupil size and object distance, and the ray diagram shows whether the image lands in front of or behind the retina. With astigmatism, each principal meridian forms its own line focus, and an eye chart and astigmatism dial are blurred to match. The tool works out the far and near points, range of clear vision, estimated acuity, spectacle power at a given vertex distance, contact lens power and the reading add. The prescription reader explains formats like “SPH −2.50 CYL −0.75 AXIS 180”. This is not medical advice.

## How to use

1. Pick a typical case (myopia, hyperopia, presbyopia, astigmatism…) or set sphere, cylinder and axis
2. Set age, pupil size and object distance, and watch where the focus falls relative to the retina
3. Switch between no correction, glasses, contacts or a reading add and compare the blurred chart and acuity
4. Paste a prescription into the reader to see plus/minus-cylinder forms, spherical equivalent and type, then load it into the simulator

## Features

- Vergence calculations on a reduced eye, with axial or refractive myopia and hyperopia
- Line foci of both principal meridians and the elliptical blur on the retina
- Eye chart and astigmatism dial blurred by defocus × pupil, with Snellen and logMAR estimates
- Far point, near point, accommodation amplitude by age (Hofstetter) and a reading-add estimate
- Vertex-distance conversion between glasses and contacts, meridian by meridian for astigmatism
- Prescription parser for English, Chinese and shorthand like −2.00/−0.50×90, with transposition

## FAQ

### How do myopia and hyperopia differ in the ray diagram?

For distant objects a normal (emmetropic) eye focuses parallel light exactly on the retina. A myopic eye has too much power for its length (a long eye or a steep cornea or lens), so the focus falls in front of the retina: distance is blurred and only objects inside the far point are sharp. It is corrected with a minus (diverging) lens. Hyperopia is the opposite: the focus falls behind the retina. Young people can pull it forward by accommodating, so they work even for distance and struggle more up close. It is corrected with a plus lens. Toggle “Eye length” vs “Optical power” to see the two causes.

### Why are glasses and contact lens powers different for strong prescriptions?

Glasses sit about 12 mm in front of the cornea, and a lens's effective power changes with position: F_cornea = F/(1 − dF). Minus lenses get stronger the farther they are from the eye, so −8.00 D glasses correspond to roughly −7.25 D contacts; plus lenses go the other way. Within about ±4 D the difference is under 0.25 D and usually ignored. For astigmatism, each principal meridian is converted separately and recombined.

### What do SPH, CYL, AXIS and ADD on a prescription mean?

SPH is the sphere power: minus for myopia, plus for hyperopia. CYL is the cylinder, which corrects astigmatism, and AXIS is its orientation from 0 to 180°. ADD is extra plus power for near vision, used for presbyopia or progressive lenses. For example, −2.50 / −0.75 × 180 means the 180° meridian needs −2.50 D and the 90° meridian needs −3.25 D. The same Rx can be written in plus-cylinder form as −3.25 / +0.75 × 90. The spherical equivalent is sphere + cylinder/2.

### What is presbyopia and how is the reading add estimated?

The lens stiffens with age, so the amplitude of accommodation falls, on average about 18.5 − 0.3 × age dioptres. Reading at 40 cm needs 2.5 D, and you can only use about half your amplitude comfortably for long, which is why near work gets hard in the early to mid forties. The tool estimates add = 1/working distance − amplitude/2, rounded up to 0.25 D. A real add also depends on your working distance and habits and is set during an eye exam.

### Can I use this to work out my own glasses?

No. It uses a simplified single-surface eye and ignores aberrations, the real shapes of the cornea and lens, binocular vision and more. The blurred chart is a geometric illustration and the acuity is a rule-of-thumb estimate. Glasses and contacts need a professional refraction and eye exam, and children with myopia, fast-changing prescriptions or any discomfort should see an eye doctor.

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