Chapter 9: Refraction by the eye Flashcards
How can the full analysis of refraction by a thick lens be simplified?
Concept of principal points and principal planes:
* a ray incident at the first principal point or plane, P1, leaves the second principal point or plane, P2, at the same vertical distance from the principal axis
What are 3 measures used to calculate the exact position of a principal point (using the thick lens formula)?
- curvature of the lens surfaces
- lens thickness
- refractive index of the lens material
How are the principal planes, principal axis and principal points relate for a thick lens?
the principal planes intersect the principal axis at right angles at the principal points
What are the nodal points of thick lens?
- there are 2 (N1 and N2) which correspond to the centre of a thin lens
- any ray directed towards the first nodal point, N1, leaves the lens as if from the second nodal point, N2, and parallel with its original direction i.e. undeviated
How are the nodal points and principal points of a thick lens related?
when the medium on both sides of the thick lens is the same, the nodal points coincide with the principal points. when the media on opposite sides are different, the nodal points do not coincide with he principal points
How are the focal length of a thick lens measured?
distance of focal lengths f1 and f2 is measured from the principal points to the principle foci
What is the definition of the principal foci?
light parallel to the principal axis is converged to or diverged from the principal foci
Wher ight the principal points of a thick lens lie?
do not lie on the surface of the lens - may lie within the lens, or outside the lens substance in meniscus form lenses
In practice, what measurement of lenses is given by instruments such as the focimeter instead of the focal length?
Anterior or posterior vertex focal length (AVFL or PVFL): the distance of the principal focus from the central surface or vertex of the lens (different from first/second focal length)
Are anterior and posterior vertex focal lengths equal to each other?
no
What calculation gives the posterior vertex power?
the reciprocal of the posterior vertex focal length, expressed in metres
What is an alternative term for the posterior vertex focal length?
back vertex power
Is the back vertex power equivalent to the focal power of the lens?
no, differs from the true focal power
Is the back vertex power equivalent to the focal power of the lens?
no, differs from the true focal power
How is the equivalent power of a thick lens calculated?
from the two surface powers plus a** correction for vergence change** due to lens thickness
What may the discrepency between equivalent and back vertex power be a cause of in thick lenses?
Cause of error in dispensing high-powered spectacle lenses, or highly curved contact lenses
What solution exists to avoid the discrepency between the equivalent and back vertex power for thick lenses?
Conversion tables
What must the second principal focus of a thick lens correspond with for a clear retinal image to be formed?
the far point of the eye
What are the 3 major refracting interfaces to be considered in the eye per the Gaussian theory of cardinal points?
Anterior corneal surface
Anterior surface of lens
Posterior surface of lens
Why is the effect of the posterior corneal surface very small?
the refractive index beween corneal stroma and aqueous is not large
What are the refractive indices of the following:
* air
* cornea
* aqueous humour
* lens (cortex-core)
* vitreous humour
- air: 1.000
- cornea: 1.376
- aqueous humour: 1.336
- lens (cortex-core): 1.386-1.406
- vitreous humour: 1.336
What is the name of the scientist who calculated the optical constants of the eye: radii of curvature, distances separating refracting surfaces and refractive indices?
What does this generate?
Gullstrand - the schematic and reduced eye calculations
How is the schematic eye, as described by Gullstrand, expressed?
in terms of its cardinal points (measured in mm behind the anterior corneal surface)
What are the nodal points of the schematic eye?
points via which rays of light pass undeviated
Why are the nodal points of the eye removed from the principal points?
because the refracting media on each side of the refracting system of the eye are different, namely air (n=1) and vitreous (n=1.336)
Where are the nodal points of the schematic eye located?
straddle the posterior pole of the crystalline lens
Why can even a small posterior polar cataract cause gross impairment of vision when the pupil is small?
the pupil only allos a small paraxial pencil of light to enter the eye, and the rays are refracted and concentrated through the nodal points and adjacent posterior lens substance
How does Listing’s schematic of the eye simplify it further than Gullstrand’s schematic?
has single principal point midway beween the two principal points of the schematic eye and same for nodal point
What is the single refracting surface power of the eye in Listing’s simplified model?
+58.6D
What is the distance of hte following in mm behind the anterior corneal surface in Listing’s simplified eye model?
* principal point
* nodal point
* first focal point
* second focal point
- principal point: 1.35
- nodal point: 7.08
- first focal point: -15.7
- second focal point: 24.13
Where is the nodal point of the eye in the simplified (Listing) version?
lies on teh posterior part of the lens
What is the power of the aphakic eye?
+43 D
What is the effective power of the crystalline lens when in situ?
+15D (58-43)
What is the actual refractive power of the lens when taken from the other refractive elements of the eye?
+ 19D
Why is the cornea refracting power much greater than the lens?
greater difference in refractive index between air (1.000) and cornea (1.376) as compared with aqueous and vitreous humour (1.336) and lens (1.406)
Why do swimmers improve blurred vision when wearing goggles underwater?
refractive index between water and ornea is only 0.040 (cornea 1.376 - water 1.336) - eliminated by keeping air in front of the cornea by goggles
What are the 2 rays that can be used to construct the image formed by parallel light incident upon the eye?
1) ray passing throuhg the anterior focus, Fa, which after refraction at the principal plane, P, continues pallel to the principal axis
2) a ray passing through the nodal point, N, undeviated
How can the size of a retinal image be calculated from a diagram from rays entering the eye?
light from the image subtends an angle, a, at the Nodal point and at the anterior focus (same angle as lines parallel). can calculate size because tan a = h/f1 (where height of image on retina = h)
What is meant by the visual angle?
angle subtended by an object at the nodal point
Why does an object appears larger as it approaches the eye?
subtends a greater visual angle as it approaches the eye
What objects could be seen by th eye if its refractive power was fixed and unalterable?
only objects at infinity
How is accommodation achieved?
ciliary muscle contraction reduces the tension on the suspensory ligament and this allows the lens to assume a more globular shape. therefore the curvatures of the lens surfaces and the lens thickness are increased, and dioptric power is increased
Where in the lens does most of the change in curvature occur during accommodation?
at the anterior lens surface (moves forwards slightly towards the cornea)
What is the definition of the far point of distinct vision?
the position of an object such that its image falls on the retina in the relaxed eye i.e. in the absence of accommodation (this is at infinity in the emmetropic eye)
What is the definition of the near point of distinct vision?
the nearest point t which an object can be clearly seen when maximum accommodation is used
What is the definition of the range of accommodation?
the distance between the far point and the near point
What is the definition of the amplitude of accommodation?
the difference in dioptric power between the eye at rest and the fully accommodated eye
What is the definition of static refraction?
the dioptric power of the resting eye
What is the definition of dynamic refraction?
the dioptric power of the accommodated eye
How can the amplitude of accommodation be calculated mathematically?
using reciprocals of near and far points distances in metres (this gives dioptric values of near and far point distances)
amplitude of accom, A = P - R
P is dioptric value of near point, R is dioptric value of far point
What is the amplitude of accommodation of an emmetropic eye with a near point of 10cm?
A = P-R
P = 1/0.1 = 10
R = 1/infinity = 0
A=10-0 = 10D
How do you calculate the accommodative power required to focus an intermediate point within range of accommodation?
A = V-R
A is accommodative power required; V is dioptric value of intermediate point; R is dioptric value of far point
What is the accommodative power required to focus an object at 1m?
A=V-R
V= 1/1 = 1
R= 1/infinity = 0
power required = 1-1 = 1D
What must eyes do in addition to accommodating to ensure clear retinal images?
must converge to maintain binocular single vision
What is the normal range for the accommodative convergence/accommodation ratio (AC/A)?
3:1 to 5:1
What is the more accurate method to measure the AC/A ratio?
Heterophoria method - measures ocular deviation for distance and near with full spectacle correction
What is the equation used to calculate AC/A?
AC/A = IPD + (Dd - Dn)/D
IPD = interpupillary disance, Dd = ocular deviation for distance, Dn= ocular deviation for near, D is near fixation distance in dioptres
What is the sign rule for values of eso and exodeviation?
positive value is esodeviation, negative is exodeviation
What is the sign rule for values of eso and exodeviation?
positive value is esodeviation, negative is exodeviation
What is the equation used to calculate the AC/A ratio that is possibly more accurate than the heterophoria method?
method uses gradient method with a minus lens rather than a near object to stimulate accommodation
AC/A = (Dd - Dn) /D
where D is the power of the minus lens used to induce accommodation
How will an abnormally high AC/A ratio be betrayed clinically?
much larger angle of esotropia for near than for distance
What may an abnormally high AC/A ratio result in?
**convergence excess esotropia **- eyes are straight for distance but break down to a convergent squint for near
Why is it important to distinguish convergence excess esotropia from esotropia that is similar for near and distance vision?
because optical and surgical managements differ
What are 2 options for the management of conergence excess esotropia?
- bifocal spectacles: distance portion incorporates full hypermetropic distance correction, near portion has further plus power
- surgery: recession of both medial recti
What are catoptric images?
four images formed by reflection at the four interfaces of the eye (anterior and posterior corneal surfaces and anterior and posterior lens surfaces) - each refracting interface also acts as a spherical mirror
What is an alternative name for the catoptric images?
Purkinje-Sanson images
What are the apparent locations of the catoptric images?
Image I and II: just behind anterior cornea
Image III and IV: within the lens
Of catoptric images I, II, III and IV, which are virtual and which are real? Which are inverted and which are erect?
image I: erect, virtual
image II: erect, virtual
image III: erect, virtual
image IV: real, inverted
What causes catoptric images to be real/virtual and erect/inverted?
I-III are formed by convex reflecting surfaces
IV is real and inverted because it is formed by a concave reflecting surface
Where does catoptric image I actually lie?
just behind the anterior lens capsule
Where does catoptric image II Actually lie?
close behind image I which is just behind the anterior lens capsule
Where does catoptric image III actually lie?
in the vitreous
Where does catoptric image IV actually lie?
anterior lens substance
What are 2 uses of catoptric image I?
- to study anterior corneal curvature (Placido’s disc for regulaity, keratometer for radius)
- diagnosis and management of squint
What information can be gained from studying catoptric images III and IV?
information re changes in lens form during accommodation
What information can be gained from studying catoptric image II alone?
specular microscopy of endothelium
