Physics of the Eye and Vision

1
Physics of the Eye and Vision

• Crystal Sigulinsky
• University of Utah Interdepartmental Program in
  Neuroscience
• Levine Lab Retinal Development
• crystal.cornett_at_utah.edu

2
Physics in Visual Processes

• Imaging in the eye
• Optics
• Absorption of light in the eye
• Quantum mechanics
• Nerve conduction
• Visual Information Processing

http//en.wikipedia.org/wiki/FileGray722.png Gray
's Anatomy of the Human Body, 1918
3
Objectives

• Optics of Imaging in the eye (Monday, June 22)
• Properties of Light
• Image Formation
• Accomodation
• The -Opias
• Glasses
• Absorption of light in the eye (Wednesday, June
  24)
• Retinal structure
• Light absorption
• Review Questions
• Nerve conduction Information Processing
  (Neuroscience Lecture, Monday, June 29)

4
Light

• Electromagnetic radiation

http//en.wikipedia.org/wiki/ImageEM_spectrum.svg
5
Properties of Light

• Wave model
• Classical sinusoidal wave
• Unique in that can travel
• through a vacuum
• Describes reflection,
• refraction, diffraction,
• interference, and Doppler Effect phenomena, etc.
• Particle model
• photon
• Describes absorption and emission phenomena

Image from http//en.wikipedia.org/wiki/ImageWave
.png
6
The eyes mediate sight

• Function
• Sensory organ for sight
• Detects light and converts it into neural
  responses that the brain interprets

Petr Novák, Wikipedia http//en.wikipedia.org/wik
i/ImageEye_iris.jpg
7
Eye Anatomy

• Anatomy
• Light enters the eye through the pupil
• Photoreceptors (light-sensing cells) are located
  in the retina
• Retina acts like the film in a camera
• GOAL to focus the image on the back of the
  retina

http//en.wikipedia.org/wiki/Eye
How are images formed?
8
Image Formation Apertures

• Apertures
• openings
• Basis of a pinhole camera
• Dark box
• small pinhole to let in light
• Image screen on opposite side of hole
• All light rays from a scene pass through single
  point (focusing)

http//en.wikipedia.org/wiki/ImagePinhole-camera.
svg
Matthew Clemente http//en.wikipedia.org/wiki/Ima
gePinhole_hydrant_neg_pos.jpg
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The Pupil is an Aperture

• Pupil
• Opening in the center of the eyeball
• Bounded by the Iris
• The iris controls the size of the pupil
• Opening through which light enters the eye

Pupil
Iris
Petr Novák, Wikipedia http//en.wikipedia.org/wik
i/ImageEye_iris.jpg
10
Image Formation Apertures

• To achieve a clear image on an image screen, the
  aperture must be very small
• Problems
• Smaller aperture
• Fewer photons get through
• Dimmer image
• Diffraction and Vignetting become significant
• Image size is large
• Solution??

Small Aperture
Large Aperture
11
Diffraction

• Apparent spreading out of waves past small
  openings

Single Slit Diffraction Pattern
http//en.wikipedia.org/wiki/FileDiffraction1.png
http//en.wikipedia.org/wiki/FileWave_Diffraction
_4Lambda_Slit.png
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Diffraction by a small aperture
http//en.wikipedia.org/wiki/FileAiry-pattern.svg
13
Vignetting

• Reduction of an images brightness at the
  periphery compared to the center
• Due to optical elements shading elements behind
  them, reducing the effective aperture

David Ball, 2007 http//en.wikipedia.org/wiki/File
Backlight-wedding.jpg
14
Lenses are the Solution to the Aperture Problems

• Lenses move the focus of the light waves past the
  aperture
• Focuses the image on the screen
• Allows for
• wider apertures
• Produces
• smaller images

Large Aperture Problem
Modified from http//en.wikipedia.org/wiki/Image
Lens3.svg
Aperture Lens Solution
15
Lenses of the Eye
http//en.wikipedia.org/wiki/Eye
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Lenses of the Eye

• Cornea
• Crystalline Lens
• Primary function focus the image on the back of
  the retina

http//en.wikipedia.org/wiki/Eye
17
Refraction

• Bending of the path of a light wave as it passes
  across the boundary separating two media
• Cause
• Change in the speed of the light wave
• No change in speed no refraction!

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Optical Density

• Optical density of a material determines the
  speed of a wave passing through it
• ? Optical density ? Speed
• How to remember this concept
• Water is more dense than air
• Harder to push yourself through water than air
• Think of walking on ground (through air) versus
  in a pool (through water)
• Harder, so you slow down

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Index of Refraction

• Abbreviated as n
• Indicator of optical density
• Indicates the number of times slower that a light
  wave would move through that material than it
  would in a vacuum.

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Refraction What direction?

• FST Fast to Slow, Towards Normal
• Low optical density, low n
• to
• high optical density, high n
• Light ray bends TOWARDS normal
• SFA Slow to Fast, Away from Normal
• High n to low n
• Light ray bends AWAY from normal

Marching Soldiers Analogy Incidence at
non-perpendicular angle to boundary
Physics Classroom Tutorial Refraction and the
Ray Model of Light http//www.ddart.net/science/ph
ysics/physics_tutorial/Class/refrn/U14L1c.html
21
Refraction What direction?

• What happens if you approach perpendicular to the
  boundary??
• NO refraction!
• Light must approach the boundary at an angle for
  refraction to occur.

Marching Soldiers Analogy Incidence at
perpendicular angle to boundary
Physics Classroom Tutorial Refraction and the
Ray Model of Light http//www.ddart.net/science/ph
ysics/physics_tutorial/Class/refrn/U14L1c.html
22
Refraction How Much?

• Snells Law
• Quantitative answer to the question of By how
  much does the light ray refract?
• nisine(?i) nrsine(?r)
• ni index of refraction of incident media
• nr index of refraction of refractive medium
• ?i angle of incidence
• ?r angle of refraction
• Angles are measured from normal

Modeled after Physics Classroom Tutorial
Refraction and the Ray Model of Light

• Greater the difference in ns, the greater the
  difference in angle of incidence and refraction
  ( more bending)
• If ni nr, then no refraction!!

23
Focusing by Lenses

• Essentially a two boundary system

http//en.wikipedia.org/wiki/FileLens2a.png
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Converging Lenses
http//en.wikipedia.org/wiki/FileLens1.svg
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Diverging Lens
http//en.wikipedia.org/wiki/FileLens1b.svg
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Focusing by Lenses

• Focal length (f)
• Quantification of the amount by which light is
  bent by the lens
• Equal to the distance at which the outgoing light
  rays intersect (focal point) when the incoming
  light rays are parallel
• Measured in meters
• By convention
• Converging lenses positive focal length
• Diverging lenses negative focal length
• Determined by
• Curvature of the lens
• Relative difference in indexes of refraction

http//en.wikipedia.org/wiki/FileLens1.svg
http//en.wikipedia.org/wiki/FileLens1b.svg
27
Refractive Power of Lenses

• focusing power of lens
• Measured in Diopters (D)
• Power (D) 1 m/f
• f focal length (meters)

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Lenses of the Eye Refractive Power

• Cornea
• Crystalline Lens

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Lenses of the Eye Refractive Power

• Cornea
• 2/3 total focusing power (39 - 48 diopters)
• Crystalline Lens
• 1/3 focusing power (15 - 24 diopters)

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Object-Image Relationship

• Image location changes depending on object
  distance for a given lens focal length
• The Lens Equation
• 1/f 1/dobject 1/dimage

Modeled after Physics Classroom Tutorial
Refraction and the Ray Model of
Light http//www.ddart.net/science/physics/physics
_tutorial/Class/refrn/U14L5db.html
f
f
2f
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Problem

• Retina is a fixed distance from the cornea-lens
  system (22 mm or 2.2 cm)
• Lens Equation
• 1/f 1/dobject 1/dimage
• In the eye,
• dimage is fixed distance between cornea lens
  system and the retina
• dobject is fixed distance between the eye and
  the object being viewed
• Solution??

32
The Solution is Accomodation

• Accomodation
• The ability of the eye to change its focal length
  (f)
• Mediated by the lens and ciliary muscles

http//en.wikipedia.org/wiki/Eye
http//hyperphysics.phy-astr.gsu.edu/Hbase/vision/
eyescal.html
33
Accomodation

• Viewing Nearby Objects
• Ciliary muscles contract
• Squeeze the lens into a more convex (fat) shape
• Pushes cornea bulge out further greater
  curvature
• C-L system has a short focal length
• High refractive power

• Viewing Distant Objects
• Ciliary muscles relaxed
• Lens assumes a flatter (skinnier) shape
• Cornea is not pushed out less curvature
• C-L system has a long focal length
• Low refractive Power

Erin Silversmith, AzaToth http//en.wikipedia.org/
wiki/ImageFocus_in_an_eye.svg
34
Far Point

• Farthest point at which an object can be brought
  into focus by the eye
• Typically is infinity
• Decreases with age

35
Near Point

• Closest point at which an object can be brought
  into focus by the eye
• Ideally 25 cm
• Finger Experiment
• Limited by the curvature of the cornea and
  adjustable radii of the lens
• Recedes with age (can lead to farsightedness)

36
The Power of Accomodation

• What is the maximum change in focusing power due
  to accomodation for a typical eye?
• Paccomodation Pfar point - Pnear point
• P 1/f
• 1/f 1/dobject 1/dimage
• Assume image distance (lens to retina) 2 cm
• 1/ffar point 1/dobject 1/dimage
• Pfar point 1/infinity 1/0.02 0 50 50 D
• 1/fnear point 1/dobject 1/dimage
• Pnear point 1/0.25 1/0.02 4 50 54 D
• Paccomodation Pfar point - Pnear point 50 D
  54 D 4 D

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Visual Defects and Correction

• Visual defects
• When an eye cannot focus an obects image on the
  retina
• Image formed in front of or behind the retina
• Results in blurred vision
• Typical causes
• Abnormal length of the eyeball
• Abnormal curvature of the cornea
• Abnormal accomodation
• Correction
• Glasses or Contact lenses

38
Hyperopia (Farsightedness)

• INABILITY of the eye to focus on NEARBY objects
• Can see far no difficulty focusing on distant
  objects
• Images of nearby objects are formed at a location
  BEHIND the retina
• Near point is located farther away from the eye

39
Hyperopia Causes

• Shortened eyeball (retina is closer than normal
  to the cornea lens system)
• Axial hyperopia
• Cornea is too flat
• Refractive hyperopia
• Lens can not assume a highly convex (fat) shape
• Refractive hyperopia

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Hyperopia Correction

• Need to refocus the image on the retina
• Decrease the focal length of the cornea-lens
  system
• Add a converging lens (positive power, D)

41
Presbyopia

• After 40 vision
• Progressively diminished ability to focus on near
  objects as one ages
• Similar to hyperopia, but different cause
• Type of refractive hyperopia
• Cause diminished power of accomodation due to
  natural process of aging
• Reduced elasticity of the lens
• Weakening of the ciliary muscles
• Changes in lens curvature due to
• continued growth

http//en.wikipedia.org/wiki/ImageSpecrx-accom.pn
g
42
Myopia (Nearsightedness)

• Inability of the eye to focus on DISTANT objects
• Can see near no difficulty focusing on nearby
  objects
• Images of distant objects are formed in front of
  the retina
• Far point is closer than normal

43
Causes of Myopia

• Not usually caused by aging
• Elongated eyeball (retina is farther away than
  normal from the cornea-lens system)
• Axial myopia
• Bulging cornea (greater curvature)
• Refractive myopia

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Correction of Myopia

• Need to refocus the image on the retina
• Increase the focal length of the cornea-lens
  system
• Add a diverging lens (negative power, -D)

45
Astigmatism

• Most common refractive error
• Blurred or sometimes distorted vision at any
  distance
• Cause
• Irregularly shaped cornea or lens
• More oblong than spherical
• Refractive power differs between regions
• Correction
• Glasses
• Lenses with different radii of curvature in
  different planes

46
Power of Corrective Eyewear

• What is the strength of lens needed to correct a
  myopic eye that has a far point of 2.0 m?
• Pcorrective Pdesired - Pactual
• P 1/f
• 1/f 1/dobject 1/dimage
• Assume image distance (lens to retina) 2 cm
• Desired
• 1/fdesired far point 1/dobject 1/dimage
• Pdesired far point 1/infinity 1/0.02 0 50
  50 D
• Actual
• 1/factual far point 1/dobject 1/dimage
• Pactual far point 1/2 1/0.02 0.5 50
  50.5 D
• Pcorrective Pdesired - Pactual 50 D 50.5 D
  -0.5 D
• Check Sign of corrective power (Does it make
  sense?)

47
Diffraction

• Apparent spreading out of waves past small
  openings

Single Slit Diffraction Pattern
http//en.wikipedia.org/wiki/FileDiffraction1.png
http//en.wikipedia.org/wiki/FileWave_Diffraction
_4Lambda_Slit.png
48
Diffraction by a small aperture
http//en.wikipedia.org/wiki/FileAiry-pattern.svg
49
More info or clarification

• crystal.cornett_at_utah.edu
• The Physics Classroom Tutorial
• http//www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/B
  Board.html

50
Review Questions

• Lecture 1 Optics

51
Question 1

• Question What is the eye?
• A. A sensory organ mediating the sense of sight
• B. A structure that detects light and converts
  it into neural responses that the brain
  interprets
• C. A structure whose anatomy is designed to
  focus light rays so that an image is formed on
  the back of the retina
• D. All of the above
• Answer D. All of the above

52
Question 2

• Question Converging lenses of the eye
• A. Include the cornea and crystalline lens
• B. Include the cornea and pupil
• C. Refract light rays to focus the image on the
  back of the retina
• D. Both A and B
• E. Both A and C
• Answer E.
• The cornea and crystalline lens are the two
  lenses of the eye. The pupil is an aperture, not
  a lens, which allows light rays to pass through
  but does not refract them. The cornea-lens
  system refracts (bends) incident light rays to
  focus the image on the back of the retina

53
Question 3

• Question Under what circumstances will
  refraction occur?
• A. When a light ray passes across any boundary
• B. When a light ray approaches at an angle to a
  boundary
• C. When a light ray changes speed due to
  entrance into a material of a different optical
  density
• D. A and B
• E. B and C
• F. All of the above
• Answer E. Both B and C are true.

54
Question 4

• Question What is the direction of refraction if
  the light wave crosses a boundary from a material
  with a high index of refraction (high n) into a
  material with a low index of refraction (low n)?
• A. Towards normal
• B. Away from normal
• Answer B.
• Solution high n high optical density slow
• low n low optical density fast
• If going from large n to small n, then going
  from slow to fast medium
• SFA if go from Slow to Fast, then bend Away
  from normal

55
Question 5

• Question You have created a new kind of plastic
  that is highly transparent and very resistant to
  scratching. It would make an excellent material
  for use in eye glasses. So, you need to know what
  the index of refraction is for this new material.
  You set up a simple experiment in which you
  measure the angles of incidence and refraction of
  a laser light as it passes from air (index of
  refraction is known) into the new plastic. What
  equation would you use to determine the index of
  refraction of your new plastic?
• A. Lens Equation
• B. Snells Law
• C. Angle Equation
• D. Refraction Law
• Answer A. Snells Law

56
Question 6

• Question Consider the phenomenon of
  accomodation. Under what condition do the ciliary
  muscles have to do the most work?
• A. When shortening the focal length of the
  cornea-lens system to view far off objects
• B. When lengthening the focal length of the
  cornea-lens system to view far off objects
• C. When shortening the focal length of the
  cornea-lens system to view objects that are
  near.
• D. When lengthening the focal length of the
  cornea-lens system to view objects that are
  near.
• Answer C.
• The focal length of the cornea lens system must
  be shortened to focus the image of a near object
  on the back of the retina. This is achieved by
  contraction of the ciliary muscles that squeeze
  the lens into a more convex (fat) shape, which in
  turn pushes on the fluid in the chamber between
  the lens and cornea causing the cornea to bulge
  out further and have a greater curvature. The
  increased curvature of the cornea and more convex
  shape of the lens refract light rays more causing
  a shortening of the focal length of the system to
  bring near objects into focus. The longest focal
  length occurs when the ciliary muscles are
  relaxed during viewing of far off objects.

57
Question 7

• Question If you took a fish out of water, would
  it exhibit hyperopia or myopia when trying to see
  in air?
• A. Hyperopia
• B. Myopia
• Answer B.
• Water has an index of refraction of 1.33
• Air has an index of refraction of 1.0003
• The index of refraction of the cornea-lens system
  is 1.37-1.4
• Both situations have light traveling from fast to
  slow so light rays will bend the same direction
  in both situations.
• Going from air to the eye is a greater change in
  the index of refraction greater change in angle
  of refraction
• So image would form in front of the retina
  Myopia

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Air, n 1.000
Cornea, n 1.376
Aqueous humor, n 1.336
Water, n 1.333
Crystalline Lens, n 1.406
Vitreous humor, n 1.336
Focus
59
Question 8

• Question How does an optometrist correct for
  hyperopia?
• A. Equips the eye with a diverging lens to
  shorten the focal length of the cornea- lens
  system
• B. Equips the eye with a diverging lens to
  lengthen the focal length of the cornea- lens
  system
• C. Equips the eye with a converging lens to
  shorten the focal length of the cornea- lens
  system
• D. Equips the eye with a converging lens to
  lengthen the focal length of the cornea- lens
  system
• Answer C.
• Hyperopia (farsightedness) occurs when the eye
  cannot focus on nearby objects because their
  images are formed behind the retina. To refocus
  the image on the retina, the focal length must be
  shortened. A shorter focal length is achieved by
  increasing the convergent refraction of the light
  rays and so a converging lens is added in front
  of the cornea lens system.

60
Power of Corrective Eyewear

• What is the strength of lens needed to correct a
  myopic eye that has a far point of 2.0 m?
• Pcorrective Pdesired - Pactual
• P 1/f
• 1/f 1/dobject 1/dimage
• Assume image distance (lens to retina) 2 cm
• Desired
• 1/fdesired far point 1/dobject 1/dimage
• Pdesired far point 1/infinity 1/0.02 0 50
  50 D
• Actual
• 1/factual far point 1/dobject 1/dimage
• Pactual far point 1/2 1/0.02 0.5 50
  50.5 D
• Pcorrective Pdesired - Pactual 50 D 50.5 D
  -0.5 D
• Check Sign of corrective power (Does it make
  sense?)

61
http//hyperphysics.phy-astr.gsu.edu/Hbase/vision/
eyescal.html