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 an optical instrument, teaching aids 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 the Gullstrand model:-

Cardinal data:-

Principal foci F1 and F2 lie 15.7 mm in front 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 the cornea.

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

The 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

Radius of curvature of the refractive surface

Anterior surface of the cornea 7.70 mm

Posterior surface of cornea 6.70mm

Anterior surface of the lens 10.00mm

Posterior surface of the lens 6.00mm

Anterior surface of lens core 7.91mm

Posterior surface of the lens core 5.76mm

THE REDUCED EYE

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

Listing’s Reduced Eye

A single principal point and a 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 treated as a single article reflecting surface. This is called Donders’ reduced eye.

Data of Donders’ reduced eye