Chapter 25: Applied Optics
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Operation of the Eye
24 mm
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Structure of the Eye
Î Essential
parts of the eye
Cornea – transparent outer
structure
‹ Pupil – opening for light
‹ Lens – partially focuses light
‹ Retina – location of image
‹ Optic nerve – sends image to
brain
‹
Î Eye
focuses light on retina
Most refraction at cornea
‹ Rest of refraction at lens
‹
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Iris Regulates Light Entering Eye
ÎThe
iris is the colored portion of the eye
‹A
muscular diaphragm controlling pupil size (regulates amount of
light entering eye)
‹ Dilates the pupil in low light conditions
‹ Contracts the pupil in high-light conditions
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Operation of Eye
Î Cornea-lens
system focuses light
onto retina (back surface)
Retina contains receptors called
rods (110M) and cones (7M)
‹ Rods & cones send impulses to
brain via optic nerve (1M fibers)
‹ Brain converts impulses into our
conscious view of the world
‹
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Picture of Retina (Seen Through Pupil)
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Rods Close Up (Retina Cross Section)
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Structure of Rods and Cones
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Color Perception in Rods and Cones
ÎOne
type of rod
Monochromatic vision
‹ Only used for night vision
‹ Highly sensitive
‹
Î3
types of cones
3 primary colors ⇒ color vision
‹ Not as sensitive as rods
‹
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The Eye: Focusing
ÎDistant
objects
‹ The
ciliary muscle is relaxed
‹ Maximum focal length of eye
ÎNear
objects
‹ The
ciliary muscles tenses
‹ The lens bulges a bit and the focal length decreases
‹ Process is called “accommodation”
ÎFocal
length of eye (normal)
≅ 16.3 mm
‹ 1/f ≅ 1 / 0.0163m = 60 “diopters” (power of lens)
‹ During accommodation, f decreases and 1/f increases
‹f
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Example of Image Size on Retina
A tree is 50m tall and 2 km distant. How big is
the image on the retina?
50 m
ÎExample:
16 mm
2 km
h′
50
=
16 2000
h'
h′ = 0.4 mm
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The Eye: Near and Far Points
ÎNear
point is the closest distance for which the lens can
accommodate to focus light on the retina
‹ Typically
at age 10, pnear ~ 18 cm (use pnear = 25 cm as average)
‹ It increases with age (presbyopia)
‹ If farsighted, then pnear > 25
ÎFar
point is the largest distance for which the lens of the
relaxed eye can focus light on the retina
‹ For
normal vision, far point is at infinity (pfar = ∞)
‹ If nearsighted, then pfar is finite
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Farsightedness (Hyperopia)
ÎThe
image focuses behind the retina
ÎSee
far objects clearly, but not nearby objects (pnear > 25 cm)
ÎNot
as common as nearsightedness
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Correcting Farsightedness
ÎA
converging lens placed in front of the eye can correct hyperopia
‹
1/f > 0, rays converge and focus on retina
ÎExample:
assume pnear = 200 cm = 2 m
What we want: see object at 25 cm (normal near point)
‹ Strategy: put object at 25 cm, make image appear at near point
‹
1 1 1
1
1
= + =
+
= 4 − 0.5 = +3.5diopters
f
p q 0.25 −2.0
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Nearsightedness (Myopia)
ÎSee
near objects clearly, but not distant objects (pfar <
ÎMost
∞)
common condition (reading, etc)
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Correcting Nearsightedness
ÎA
diverging lens can be used to correct the condition
‹
1/f < 0, rays diverge (spread out) and focus on retina
Î Example:
assume pfar = 50 cm = 0.5 m
What we want: see objects at infinity (normal far point)
‹ Strategy: if object at infinity, make image appear at eye’s far point
‹
1 1 1 1
1
= + = +
= −2.0diopters
f
p q ∞ −0.5
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Presbyopia and Age
Î Presbyopia
is due to a reduction in
accommodation range
Accommodation range is max for
infants (60 – 73 diopters)
‹ Shrinks with age, noticeable effect
on reading after 40
‹ Can be corrected with converging
lenses (reading glasses)
‹
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Magnifier
ÎConsider
small object held in front of eye
‹ Height
y
‹ Makes
an angle θ at given distance from the eye
ÎGoal
is to make object “appear bigger” ⇒ Larger θ
y
θ
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Magnifier
ÎSingle
converging lens
‹ Simple
analysis: put eye right behind lens
‹ Put object at focal point and image at infinity
‹ Angular size of object is θ′, bigger!
θ′
y
f
Image at infinity
q=∞
p=f
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Angular Magnification (Simple)
ÎWithout
magnifier: 25 cm is closest distance to view
‹ Defined
by average near point (younger people can do closer)
‹ θ ≈ tanθ = y / 25
ÎWith
magnifier: put object at distance p = f
‹ Image
at infinity
‹ θ' ≈ tanθ' = y / f
ÎDefine
“angular magnification” mθ = θ' / θ
y
y
θ
θ′ 25
f
θ ′ 25
mθ = =
f
θ
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Angular Magnification (Maximum)
ÎCan
do better by bringing object closer to lens
1
1
1
‹ Put image at near point, q = −25 cm
+
=
p −25 f
ÎAnalysis
‹θ
≈ tanθ = y / 25
‹ θ' ≈ tanθ' = y / p
‹ mθ = θ' / θ = 25 / p
1 1 1
= +
p f 25
25 25
=
+1
mθ =
p
f
Outgoing
rays
θ′
f
y
f
PHY2054: Chapter 25
Rays seen coming from
near point. Can’t bring
any closer!
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Example
ÎFind
angular magnification of lens with f = 4 cm
25
= 6.3
Simple
mθ =
4
25
+ 1 = 7.3 Maximum
mθ =
4
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Example: Image Size of Magnifier
ÎHow
big is projected image of sun?
‹ Sun
is 0.5° in diameter (0.0087 rad)
‹ Image located at focal point. (Why?)
‹ Assume f = 5 cm
‹ Size is f × θ = 5 × 0.0087 = 0.0435 cm
ÎEnergy
concentration of 10 cm lens?
‹ All
solar rays focused on image
‹ Energy concentration is ratio of areas
‹ Concentration = (10 / 0.0435)2 = 53,000!
‹ Principle of solar furnace (mirrors)
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Projectors
ÎIdea:
ÎPut
project image of slide onto distant screen
slide near focal point of lens
‹ Upside
down to make image upright
Screen
Lens
pf
q=
p− f
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Projector Example
ÎProblem
‹ Lens
of 5 cm focal length
‹ Lens is 3 m from screen
‹ Where and how should slide be placed?
ÎSolution:
real image required. Why?
‹q
= 3 m = +300 cm
‹ f = 5 cm
‹ Find p from lens equation
1 1 1
= −
p f q
300 )( 5)
(
qf
p=
=
= 5.085 cm
q− f
300 − 5
ÎSo
5.085 cm from lens, just past focal point
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