Laws in Ophthalmology: Hering to Poiseuille in Tables
Last updated: October 2026
Laws come up in vivas because each explains a clinical observation. Here they are grouped into eye movements, optics and visual physiology, with what each law means at the bedside.
Eye movements
| Law | Statement | Clinical meaning |
|---|---|---|
| Hering's law of equal innervation | Yoke muscles of the two eyes receive equal innervation ("one impulse directs both eyes, as a pair of horses is driven with single reins") | Secondary deviation (fixing with the paretic eye) is larger than the primary deviation |
| Sherrington's law of reciprocal innervation | Contraction of a muscle is accompanied by relaxation of its antagonist in the same eye | Explains Duane syndrome co-contraction when the law is broken by miswiring |
| Donders' law | For each direction of gaze, the eye has one fixed torsional orientation, whatever path it took to get there | Removes the extra degree of freedom of eye rotation |
| Listing's law | Every eye position can be reached from primary position by rotation about a single axis lying in Listing's (equatorial) plane | Basis of Donders' law; broken in some motility disorders |
| Alexander's law | Jerk nystagmus is strongest when looking in the direction of the fast phase | Classic for peripheral vestibular nystagmus |
Optics
| Law | Statement | Clinical meaning |
|---|---|---|
| Snell's law | n₁ sin θ₁ = n₂ sin θ₂: light bends towards the normal entering a denser medium and away from it leaving | Total internal reflection at the cornea is why the angle needs a goniolens |
| Knapp's law | A correcting lens placed at the anterior focal point of the eye (about 15 mm) gives a retinal image of the same size as in an emmetrope (for axial ametropia) | Axial anisometropia tolerates spectacles; the same principle is the Badal (optometer) principle in lensmeters |
| Prentice's rule | Prism (Δ) = decentration (cm) × lens power (D) | Induced prism from decentred lenses; vertical imbalance in anisometropic bifocal wearers |
| Inverse square law | Illuminance falls with the square of the distance from a point source | Distance and brightness of test lights |
More: Clinical optics made easy
Visual physiology and blood flow
| Law | Statement | Clinical meaning |
|---|---|---|
| Weber's law | The just-noticeable increment in light is a constant fraction of the background: ΔI / I = constant (Weber fraction) | Contrast threshold stays steady over a wide range of light levels, so pupil size has little effect on threshold in photopic conditions |
| Bloch's law (time–intensity reciprocity) | B × t = K: below a critical duration (about 100 ms), a brief bright flash and a longer dim flash look equally bright | Basis of stimulus duration in perimetry |
| Ricco's law (area–intensity) | I × A = K for small stimuli below a critical area | Why Goldmann stimulus size matters in perimetry |
| Dowling–Rushton relation | log (threshold / dark-adapted threshold) is proportional to the fraction of pigment still bleached | Threshold recovers logarithmically as rhodopsin regenerates during dark adaptation |
| Hagen–Poiseuille law | Flow = pressure ÷ resistance, where resistance = 8ηL / πr⁴ | Halving a vessel's radius cuts flow sixteen-fold; aqueous outflow and retinal blood flow |
| Murray's law | In an efficient vascular tree, the cube of a parent vessel's radius equals the sum of the cubes of its branches | Retinal vessel branching analysis |
Where residents slip
- Mixing up Hering and Sherrington: Hering is between the two eyes (yokes), Sherrington is within one eye (agonist and antagonist).
- Stating Knapp's law for refractive ametropia: it holds for axial ametropia only.
- Forgetting that resistance depends on r⁴: a small narrowing has a big effect on flow.
Related: Formulas in ophthalmology, Ocular motility made easy, Clinical optics made easy.
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