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Schematic Eye and Reduced Eye

  • schematic eye :-

-Schematic eye is a physical or mathematical model that represents the basic optical feature of the real eye.                   

  • Objectives:-

To provide a basis for the theoretical studies of the eye as a optical instrument , teaching aid in optics, optometry, ophthalmology , vision and visual perception.

  • History:-

Listing and Gauss while studying refraction by lens combination, concluded that for a homocentric lenses system there exist three pairs of cardinal points

1.two principal foci

2.two principal points

3. two nodal points

These all are situated on the principal axis of the system. The models of schematic eyes developed by Listing, Tscherning, and Helmholtz greatly advanced the understanding of the optics of the eye .

However, Gullstrand developed the most authoritative model of the eye .

  • According to Gullstrand model :-
  • Cardinal data:-

Principal foci F1 and F2 lie 15.7 mm infront and 24.4 mm behind the cornea.

Principal points P1 and P2 lie in the anterior chamber 1.35 mm and 1.60 mm behind the anterior surface of cornea.

Nodal points N1 and N2 lie in the posterior part of lens 7.08 mm and 7.33 mm behind the anterior surface of the cornea.

Total dioptric power of this schematic eye is 58.64D.

  • Refractive indices:-

Cornea                   1.376

Aqueous                1.336

Lens cortex          1.386

Lens Core             1.406

Vitreous                1.336

  • Radious of curvature of the refractive surface

Anterior surface of cornea     7.70 mm

Posterior surface of cornea     6.70mm

Anterior surface of the lens     10.00mm

Posterior surface of lens          6.00mm

Anterior surface of lens core    7.91mm

Posterior surface of lens core    5.76mm


   The reduced eye is an idealized Model of the optics of the human eye. Listing and Donders has                simplified the reduced eye .

■Listing’s Reduced Eye

Single principal point and single nodal point lying midway between two principal points and two nodal points , respectively is called Listing’s reduced eye.

Data of Listing’s reduced eye :

Principle Point  (P) lies 1.5 mm behind the anterior surface of cornea.

• Nodal point (N) is situated 7.2 mm behind the anterior surface of cornea.

• Anterior focal point (F¹) is 15.7 mm in front of the anterior surface of the cornea.

• Posterior focal point (F2) s 24.4 mm behind the anterior surface of the cornea .

• Anterior focal length (f¹) is 17.2 mm (15.7 +1.5)

 • Posterior focal point(F2) is 22.9 mm (24.4- 1.5)

• Total dioptric power of the reduced eye is about  +60 D ( +43D is cornea and +17D crystalline lens).

Drawing –

■Donders’ Reduced Eye

The optical system of the eye is bring treated as a single article reflecting surface . This is called Donders’ reduced eye .

Data of Donders’ reduced eye

• Principle point lies 2 mm behind the corner with a radius of curvature of 5mm

•Nodal point is situated 5mm  behind the plane .

•Anterior focal(f1) length  is a 15 mm •Posterior focal (f2) length is 20mm •Refractive index is 1.336

•Total power is +60D

◇ Significance of the reduced eye –

▪︎ Designing the instrument

▪︎ Making calculation

▪︎ Localizing a foreign body

▪︎ Derived formula for the intraocular lens power

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This Post Has 4 Comments

  1. Anneswa Ganguly

    Thank you so much ma’am for sharing your knowledge.

  2. Sagata Saha

    Very informative and interesting