The document discusses refraction in the human eye. It describes the three main refracting interfaces - the anterior corneal surface and two lens surfaces. It provides tables of refractive indices of ocular media, positions and radii of curvature of refracting surfaces based on Gullstrand's measurements. It introduces the schematic eye model and reduced eye model, listing their optical parameters including principal points, nodal points, focal lengths. It describes how the reduced eye can be used to construct retinal images and relate image size to the visual angle subtended at the nodal point.

3. 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 .

4. 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 .

5. 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

6. oIn 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 ,

7. 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

8. 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

9. 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.

10. The Schematic Eye:
oIn 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)

11. oTable 1.4
First 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)

12. 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 )

13. 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

14. oProduces gross impairment of vision when the
pupil is small
oDiagram:

15.  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 .

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

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

18. 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 .

19. 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 ) .

20. 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.

21. 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 .

22. 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

23. 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

24. 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 ∝= ℎ
𝑓1, the retinal image size
h = tan ∝ × 𝑓1 .
oThe angle ∝ subtended by an object at the
nodal point is called visual angle .

25. • Diagram :
●
N F2
hh
●
Fa
∝
∝
∝
f1