Human Eye Optics Simulator
Model the human eye as a lens system. See how near-sightedness and far-sightedness arise and how corrective lenses fix the focal point on the retina.
The Human Eye as an Optical System
The eye forms images using two main refracting surfaces: the cornea (which provides about 2/3 of total power) and the crystalline lens (which provides the remaining adjustable 1/3). Together they act as a converging lens system that focuses light onto the retina, the photosensitive layer at the back of the eye.
Normal Vision
In a normal (emmetropic) eye, parallel rays from a distant object are focused exactly on the retina without any accommodation. The far point (the farthest distance at which the relaxed eye can focus) is at infinity, and the near point (closest comfortable focus) is about 25 cm.
Myopia (Near-Sightedness)
In a myopic eye, the eyeball is too long or the cornea too curved, so parallel rays converge in front of the retina. Distant objects appear blurry. The far point is closer than infinity — for example 50 cm means only objects within 50 cm can be seen clearly without correction.
Correction uses a diverging (concave) lens of power P = −1/d_far (in metres). This shifts the effective far point to infinity.
Hyperopia (Far-Sightedness)
In a hyperopic eye, the eyeball is too short, so parallel rays would converge behind the retina. Near objects appear blurry because additional accommodation is needed even for normal viewing distances. The near point is farther than the standard 25 cm.
Correction uses a converging (convex) lens. The required power brings the near point back to 25 cm.
| Condition | Focal Problem | Corrective Lens | Power Sign |
|---|---|---|---|
| Normal | Focuses on retina | None needed | — |
| Myopia | Focuses in front of retina | Diverging (concave) | Negative (−) |
| Hyperopia | Focuses behind retina | Converging (convex) | Positive (+) |
Eye Optics Formulas
Lens Power
Power P is measured in diopters (D = m⁻¹). A positive power converges light; a negative power diverges it.
Myopia Correction
Hyperopia Correction
Here 0.25 m is the standard near point (25 cm) and d_near is the patient's uncorrected near point in metres.
Thin Lens Equation
| Symbol | Meaning | Unit |
|---|---|---|
| f | Focal length of corrective lens | m |
| P | Lens power | diopters (D = m⁻¹) |
| d_far | Far point (myopia) | m |
| d_near | Near point (hyperopia) | m |
| d_o | Object distance | m |
| d_i | Image distance | m |
Frequently Asked Questions
Why is myopia corrected with a negative (diverging) lens?
A myopic eye focuses too strongly — rays converge before reaching the retina. A diverging lens pre-spreads the rays so that the eye's own optics then focus them exactly on the retina. The diverging lens has a focal length equal to the patient's far point distance, giving a negative power.
What does −2.5 diopters mean on a glasses prescription?
It means the corrective lens has a focal length of f = 1/|P| = 1/2.5 = 0.4 m = 40 cm. It is a diverging lens for myopia correction. The unaided far point of that eye is 40 cm.
Why is 25 cm used as the standard near point?
25 cm (250 mm) is the conventional 'least distance of distinct vision' for a healthy young adult eye. It is the reference distance used in optics problems and for calculating hyperopia correction.
Can myopia and hyperopia occur in the same eye?
Yes — astigmatism often accompanies either condition, and some people are myopic in one eye and hyperopic in the other (anisometropia). Astigmatism is corrected with a cylindrical lens component not modelled in this simulator.
Why does uncorrected hyperopia worsen with age?
Young hyperopic patients can use accommodation (lens flattening/bulging via ciliary muscles) to compensate. As the lens stiffens with age (presbyopia), accommodation decreases and the hyperopia becomes fully symptomatic, requiring reading glasses.