chapter 25: applied optics
Post on 23-Mar-2022
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PHY2054: Chapter 25 3
Structure of the EyeEssential parts of the eye
Cornea – transparent outer structurePupil – opening for lightLens – partially focuses lightRetina – location of imageOptic nerve – sends image to brain
Eye focuses light on retinaMost refraction at corneaRest of refraction at lens
PHY2054: Chapter 25 4
Iris Regulates Light Entering EyeThe iris is the colored portion of the eye
A muscular diaphragm controlling pupil size (regulates amount oflight entering eye)Dilates the pupil in low light conditionsContracts the pupil in high-light conditions
PHY2054: Chapter 25 5
Operation of EyeCornea-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
PHY2054: Chapter 25 9
Color Perception in Rods and ConesOne type of rod
Monochromatic visionOnly used for night visionHighly sensitive
3 types of cones3 primary colors ⇒ color visionNot as sensitive as rods
PHY2054: Chapter 25 10
The Eye: FocusingDistant objects
The ciliary muscle is relaxedMaximum focal length of eye
Near objectsThe ciliary muscles tensesThe lens bulges a bit and the focal length decreasesProcess is called “accommodation”
Focal length of eye (normal)f ≅ 16.3 mm1/f ≅ 1 / 0.0163m = 60 “diopters” (power of lens)During accommodation, f decreases and 1/f increases
PHY2054: Chapter 25 11
Example of Image Size on RetinaExample: A tree is 50m tall and 2 km distant. How big is the image on the retina?
2 km
50 m
16 mm
h'
5016 2000h′
= 0.4mmh′ =
PHY2054: Chapter 25 12
The Eye: Near and Far PointsNear 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
Far 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
PHY2054: Chapter 25 13
Farsightedness (Hyperopia)
The image focuses behind the retina
See far objects clearly, but not nearby objects (pnear > 25 cm)
Not as common as nearsightedness
PHY2054: Chapter 25 14
Correcting Farsightedness
A converging lens placed in front of the eye can correct hyperopia1/f > 0, rays converge and focus on retina
Example: assume pnear = 200 cm = 2 mWhat 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 3.5diopters0.25 2.0f p q
= + = + = − = +−
PHY2054: Chapter 25 15
Nearsightedness (Myopia)
See near objects clearly, but not distant objects (pfar < ∞)Most common condition (reading, etc)
PHY2054: Chapter 25 16
Correcting Nearsightedness
A diverging lens can be used to correct the condition1/f < 0, rays diverge (spread out) and focus on retina
Example: assume pfar = 50 cm = 0.5 mWhat 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 2.0diopters0.5f p q
= + = + = −∞ −
PHY2054: Chapter 25 17
Presbyopia and AgePresbyopia 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 40Can be corrected with converging lenses (reading glasses)
PHY2054: Chapter 25 18
MagnifierConsider small object held in front of eye
Height yMakes an angle θ at given distance from the eye
Goal is to make object “appear bigger” ⇒ Larger θ
y
θ
PHY2054: Chapter 25 19
MagnifierSingle converging lens
Simple analysis: put eye right behind lensPut object at focal point and image at infinityAngular size of object is θ′, bigger!
yθ ′f Image at infinity
q = ∞p = f
PHY2054: Chapter 25 20
Angular Magnification (Simple)Without magnifier: 25 cm is closest distance to view
Defined by average near point (younger people can do closer)θ ≈ tanθ = y / 25
With magnifier: put object at distance p = fImage at infinityθ' ≈ tanθ' = y / f
Define “angular magnification” mθ = θ' / θ
2525
y yf
mfθ
θ θ
θθ
′
′= =
PHY2054: Chapter 25 21
Angular Magnification (Maximum)Can do better by bringing object closer to lens
Put image at near point, q = −25 cm
Analysisθ ≈ tanθ = y / 25θ' ≈ tanθ' = y / pmθ = θ' / θ = 25 / p
Outgoingrays
Rays seen coming fromnear point. Can’t bringany closer!
θ′ff
1 1 125
1 1 125
25 25 1
p f
p f
mp fθ
+ =−
= +
= = +
y
PHY2054: Chapter 25 22
ExampleFind angular magnification of lens with f = 4 cm
25 6.3 Simple425 1 7.3 Maximum4
m
m
θ
θ
= =
= + =
PHY2054: Chapter 25 23
Example: Image Size of MagnifierHow big is projected image of sun?
Sun is 0.5° in diameter (0.0087 rad)Image located at focal point. (Why?)Assume f = 5 cmSize is f × θ = 5 × 0.0087 = 0.0435 cm
Energy concentration of 10 cm lens?All solar rays focused on imageEnergy concentration is ratio of areasConcentration = (10 / 0.0435)2 = 53,000!Principle of solar furnace (mirrors) f
PHY2054: Chapter 25 24
ProjectorsIdea: project image of slide onto distant screen
Put slide near focal point of lensUpside down to make image upright
ScreenLens
pfqp f
=−
PHY2054: Chapter 25 25
Projector ExampleProblem
Lens of 5 cm focal lengthLens is 3 m from screenWhere and how should slide be placed?
Solution: real image required. Why?q = 3 m = +300 cmf = 5 cmFind p from lens equation
So 5.085 cm from lens, just past focal point
1 1 1p f q= −
( )( )300 55.085 cm
300 5qfp
q f= = =
− −
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