chapter 25: applied optics

PHY2054: Chapter 25 1

Chapter 25: Applied Optics


Operation of the Eye

24 mm


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


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


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


Picture of Retina (Seen Through Pupil)


Rods Close Up (Retina Cross Section)


Structure of Rods and Cones


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


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


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′ =


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


Farsightedness (Hyperopia)

The image focuses behind the retina

See far objects clearly, but not nearby objects (pnear > 25 cm)

Not as common as nearsightedness


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

= + = + = − = +−


Nearsightedness (Myopia)

See near objects clearly, but not distant objects (pfar < ∞)Most common condition (reading, etc)


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

= + = + = −∞ −


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)


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


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


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

′

′= =


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


ExampleFind angular magnification of lens with f = 4 cm

25 6.3 Simple425 1 7.3 Maximum4

m

m

θ

θ

= =

= + =


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


ProjectorsIdea: project image of slide onto distant screen

Put slide near focal point of lensUpside down to make image upright

ScreenLens

pfqp f

=−


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= = =

− −

chapter 25: applied optics

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