The Physics of Sight

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The Physics of Sight

• Crystal Sigulinsky
• University of Utah Interdepartmental Program in
  Neuroscience
• crystal.cornett_at_utah.edu

2
Objectives

• The eye
• Image Formation
• Apertures
• Lenses
• Accomodation
• Nearsightedness and Farsightedness
• Glasses

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Sight
4
The eyes mediate sight

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

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Eye Anatomy

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

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The Pupil is an Aperture

• Apertures
• openings
• 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
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Image Formation Apertures

• 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
• Focuses the light

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Image Formation Apertures

• To achieve a clear image on an image screen, the
  aperture must be very small
• Problems
• Image screen must be large
• Eye would have to be massive
• Smaller aperture results in a dimmer image
• Less photons get through

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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 wider apertures
• Produces smaller images

Large Aperture Problem
Aperture Lens Solution
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Lenses of the Eye

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

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Refraction

• Bending of the path of a light wave as it passes
  across the boundary separating two media
• Caused by a change in the speed of the light wave
• No change in speed No change in direction of
  the line

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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.

Material Index of Refraction
Vacuum 1.0000
Air 1.0003
Ice 1.31
Water 1.33
Crown Glass 1.52
Flint Glass 1.58-1.66
Diamond 2.417
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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

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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

• If ni nr , then no refraction!!

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Refraction in Converging lenses
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Lenses Image Formation

• Three Rules of Refraction for a Double Convex
  Lens
• Any incident ray traveling parallel to the
  principal axis of a converging lens will refract
  through the lens and travel through the focal
  point on the opposite side of the lens.
• Any incident ray traveling through the focal
  point on the way to the lens will refract through
  the lens and travel parallel to the principal
  axis.
• An incident ray which passes through the center
  of the lens will in effect continue in the same
  direction that it had when it entered the lens.
• Image is inverted (flipped horizontally over the
  principle axis)

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Problem

• Image location changes depending on object
  distance
• Retina is a fixed distance from the cornea-lens
  system (22 mm or 2.2 cm)

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The Solution is Accomodation

• The Lens Equation
• 1/f 1/dobject 1/dimage
• Accomodation
• The ability of the eye to change its focal length
  (f)
• Mediated by the lens and ciliary muscles

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Accomodation

• Nearby Objects
• Have a longer dimage
• Shorten the focal length
• Ciliary muscles contract
• Squeeze the lens into a more convex (fat) shape
• Pushes cornea bulge out further greater
  curvature

• Distant Objects
• Have a shorter dimage
• Lengthen the focal length
• Ciliary muscles relax
• Lens assumes a flatter (skinnier) shape
• Cornea is not pushed out less curvature

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Near Point

• Closest point at which an object can be brought
  into focus by the eye
• Finger Experiment
• Limited by the curvature of the cornea and
  adjustable radii of the lens
• Typically about 25 cm
• Decreases with age

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Far Point

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

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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

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Causes of Hyperopia

• Shortened eyeball (retina is closer than normal
  to the cornea lens system)
• Lens can no longer assume highly convex (fat)
  shape
• Accomodation no longer working
• Weakened ciliary muscles
• Reduced flexibility of the lens
• Common as people age

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Correction of Hyperopia

• Need to refocus the image on the retina
• Decrease the focal length of the cornea lens
  system
• More refraction
• Add a converging lens

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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

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Causes of Myopia

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

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Correction of Myopia

• Need to refocus the image on the retina
• Increase the focal length of the cornea lens
  system
• Less refraction
• Add a diverging lens

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Question 1

• Question What is the eye?
• A. Sensory organ for 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 an image on the back of the retina
• D. All of the above
• Answer D. All of the above

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Question 2

• Question How do apertures form images?
• A. By focusing light rays
• B. By refracting light rays
• C. By confining all rays from a scene through a
  single point
• D. Both A and B
• E. Both A and C
• Answer E. confining all rays from a scene
  through a single point focuses these rays to form
  an image

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Question 3

• 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
  aperature, 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

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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

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Question 5

• Question Calculate the angle of refraction (?r
  ) for the given boundary situation if the angle
  of incidence (?i) 45

• Answer ?r 32
• Solution
• -Use Snells Law
• nisine(?i) nrsine(?r)

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Question 6

• Using the 3 rules of refraction for a double
  convex lens, draw the image of the given object
  that would be formed by the following lens

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Question 6 (Solution)

• Step 1.
• Determine the position of the image point
  corresponding to the top of the object ()

• Step 2.
• Determine the position of the image point
  corresponding to the bottom of the object ()

Object
Object
F
2F
2F
F



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Question 6 (Answer)

• Step 3.
• Fill in the image knowing that the indicates
  the position of the top of the image and the
  indicates the position of the bottom of the image

• Correct Image Drawing

Object
Object
F
2F
2F
F
F
2F
2F
F
Image


Image
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Question 7

• Question What is involved in the accomodation
  for nearby objects (image distance is longer than
  the distance between the retina and the cornea
  lens system)?
• A. Focal length of the cornea lens system is
  shortened
• B. Ciliary muscles relax to make the lens
  skinnier
• C. Cornea has a greater curvature due to
  bulging
• D. A and C
• E. B and C
• Answer D. The focal length of the cornea lens
  system must be shortened to focus the image 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

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Question 8

• Question How does an optometrist correct for
  hyperopia?
• A. Equips the eye with a diverging lens to
  increase refraction of light rays
• B. Equips the eye with a diverging lens to
  decrease refraction of light rays
• C. Equips the eye with a converging lens to
  increase refraction of light rays
• D. Equips the eye with a converging lens to
  decrease refraction of light rays
• 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 refraction
  of the light rays and so a converging lens is
  added in front of the cornea lens system.