Refraction by the EyeThe schematic EyeThe Reduced Eye

BY Kausar Ali Student At

Doctor of Optometry PEF University College

PESHAWAR

Refraction By the Eye :oThe foregoing analysis of refraction by a thick

lens is just one application of the Gaussian theory of the cardinal points .

oThe theory may be applied to any system of coaxial spherical refracting surfaces including the human eye .

oThere are three major refracting interfaces to be consider in the eye Anterior corneal and two surfaces of the lens .

oThe effect of the posterior corneal surface is very small compared with these three .

oThe difference in the refractive index between corneal stroma and aqueous is not large .

oRefractive indices of the transparent media of the eye (Gullstrand ) TABLE 1.1

Air 1.000

cornea 1.376

Aqueous humour 1.336

Lens ( cortex – core ) 1.386 – 1.406

Vitreous humour 1.336

o In order to calculate the cardinal points, the radii of curvature, and distances separating the refracting surfaces must also be known .

oThese have been determined experimentally by several observers .

oAs in the case of any anatomical measurement there is some physiological variation and the values are given are the means ,

oGullstrand Table 1.2:o1.2 : position of refracting surfaces of the eye

(in mm behind interior corneal surface )Cornea anterior surface 0 mm

Cornea posterior surface 0.5 mm

Lens anterior surface 3.6 mm

Lens posterior surface 7.2 mm

Lens core anterior surface 4.146

Lens core posterior surface 6.565

oTable 1.3 Radii of curvature of refracting surfaces of the eye in ( mm ) (Gullstrand)

Cornea anterior surface 7.7 mm

Cornea posterior surface 6.8mm

Lens anterior surface 10mm

Lens posterior surface - 6.0 mm

Lens core anterior surface 7.9mm

Lens core posterior surface - 5.76

oGiven calculation of the schematic and reduced eye are based .

oThese measurements are know as the optical constant of the eye .

oSeveral sets of measurement are available from other observers which differs slightly one from other .

oNo one set is in general standard use.

The Schematic Eye: o In the schematic eye , as described by

Gullstrand .oThe refracting system is expressed in terms of

its cardinal points ( measured in mm behind the anterior corneal surface )

oSchematic eye, cardinal points , ( Gullstrand)

oTable 1.4First principal point P1 1.35

Second principal point P2 1.60

First nodal point N1 7.08

Second nodal point N2 7.33

First focal point -15 .7

Second focal point 24.4

Refractive power 58.64 D

Calculated by Percival ( 1928)

oThe nodal points, via which rays of light pass un deviated .

oThe principal points , lei at the intersection of the principal planes with the principal axis .

oNodal points are removed from principal points. oRefracting media on each side of the refracting

system of the eyes are different, namely Air (n =1) and vitreous (n = 1.336 )

oThe nodal point straddle the posterior pole of the crystalline lens .

oThe pupil of the eye allows only a relatively small paraxial pencil .

oSuch paraxial rays are refracted and concentrated through the nodal points and adjacent posterior lens substances .

oTherefore even a small posterior polar cataract

oProduces gross impairment of vision when the pupil is small

oDiagram:

The Reduced Eye : o1853 who chose a single principal point lying

midway between the two principal points of the schematic eye .

oA single nodal point was postulated in the same way .

oFocal length adjusted with reference to the new principal point .

oThe result is the Reduced eye in which the eye is treated as a single refracting surface of power +58 D.

oDiagram:

oMany sets of figures exist for the reduced . Those quoted here are based on Gullstrand's data.

o It must be emphasized that the distance given for the focal point are measured from anterior corneal surface .

oTable 1.5 the reduced eye ( distance in mm behind anterior corneal surface )

Principal point p 1.35

Nodal point N 7.08

First focal point -15.7

Second focal point 24.13

o The corresponding focal length, measured from the principle point, are – 17 .05 mm and 22.78 mm .

oNote that the nodal point lies in the posterior part of the lens, while the second focal point lies 24.13 mm behind the cornea i-e on the retina of normal eye .

oThe anterior focal length of the aphakic eye was found experimentally to be – 23.23 mm ( the first focal point lying 21.88 mm in front of cornea ) .

oThis give a calculated power of +43 D for the aphakic eye .

oThe crystalline lens thus in effective power of +15 D .

oThe cornea is the only refracting element remaining in the eye power of +43 D .

o cornea have greater refractive power because of the greater refractive index difference between the air 1.000 and cornea which is 1.376.

o Reduced Eye – Construction of retinal image : oUsing the reduced eye, it is simple to construct

the retinal image formed under various condition .

oThe reduced eye itself is represented by two parallel lines , which indicate the principle plane p, and the retina R, These intersect principle axis ( Optical axis ) at right angles .

oThe nodal point N is indicated by a point as is the anterior focus Fa . The second principle focus F2 falls on the retina in the emmetropic eye. P R

●N●Fa

Reduced Eye – image formation

oTwo rays are used to construct image formed by parallel light incident upon the eye .

o (1) A ray passing through anterior focus, Fa, which after refraction at the principle plane P, continue parallel to the principle axis .

o (2) A ray passing through the nodal point ,N’ un deviated .

oThe size of the retinal image may be also

oFrom the same construction . It can be seen that the light subtends angle at the nodal point N, as well as the anterior focus , fa Retinal image size is there fore directly related to the angle subtended by an object at the nodal point (f1 being constant in the individual eye ) . Because tan, the retinal image size h = tan .

oThe angle subtended by an object at the nodal point is called visual angle .

• Diagram :

●N F2

hh

●Fa

∝∝∝f1

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