eye

Physics of the Eye and Physics of the Eye and VisionVision

Crystal SigulinskyCrystal Sigulinsky

University of Utah: Interdepartmental University of Utah: Interdepartmental Program in NeuroscienceProgram in Neuroscience

Levine Lab: Retinal DevelopmentLevine Lab: Retinal Development

[email protected]@utah.edu

Physics in Visual Physics in Visual ProcessesProcesses

Imaging in the eyeImaging in the eye OpticsOptics

Absorption of light in Absorption of light in the eyethe eye Quantum mechanicsQuantum mechanics

Nerve conduction Nerve conduction Visual Information Visual Information

ProcessingProcessinghttp://en.wikipedia.org/wiki/File:Gray722.pngGray's Anatomy of the Human Body, 1918

http://en.wikipedia.org/wiki/File:Gray722.png

ObjectivesObjectives

Optics of Imaging in the eye (Monday, June 22)Optics of Imaging in the eye (Monday, June 22) Properties of LightProperties of Light Image FormationImage Formation AccomodationAccomodation The “-Opias” The “-Opias” GlassesGlasses

Absorption of light in the eye (Wednesday, June 24)Absorption of light in the eye (Wednesday, June 24) Retinal structure Retinal structure Light absorptionLight absorption

Review Questions Review Questions Nerve conduction & Information Processing Nerve conduction & Information Processing

(Neuroscience Lecture, Monday, June 29)(Neuroscience Lecture, Monday, June 29)

LightLight

Electromagnetic radiationElectromagnetic radiation

http://en.wikipedia.org/wiki/Image:EM_spectrum.svg

Properties of LightProperties of Light

Wave modelWave model Classical sinusoidal waveClassical sinusoidal wave

Unique in that can travel Unique in that can travel

through a vacuumthrough a vacuum

Describes reflection, Describes reflection,

refraction, diffraction, refraction, diffraction,

interference, and Doppler Effect phenomena, etc.interference, and Doppler Effect phenomena, etc.

Particle modelParticle model ““photon” photon” Describes absorption and emission phenomenaDescribes absorption and emission phenomena

Image from http://en.wikipedia.org/wiki/Image:Wave.png

The eyes mediate sightThe eyes mediate sight

FunctionFunction Sensory organ for sight Sensory organ for sight Detects light and converts it into neural responses that the Detects light and converts it into neural responses that the

brain interpretsbrain interprets

Petr Novák, Wikipedia http://en.wikipedia.org/wiki/Image:Eye_iris.jpg

Eye AnatomyEye Anatomy

AnatomyAnatomy Light enters the eye Light enters the eye

through the pupil through the pupil Photoreceptors (light-Photoreceptors (light-

sensing cells) are sensing cells) are located in the retinalocated in the retina

Retina acts like the film Retina acts like the film in a camerain a camera

GOAL: to focus the GOAL: to focus the image on the back of image on the back of the retinathe retina

http://en.wikipedia.org/wiki/Eye

How are images formed?How are images formed?

Image Formation: AperturesImage Formation: Apertures

AperturesApertures ““openings”openings”

Basis of a pinhole Basis of a pinhole cameracamera Dark box Dark box

small “pinhole” to let in small “pinhole” to let in lightlight

Image screen on Image screen on opposite side of holeopposite side of hole

All light rays from a All light rays from a scene pass through scene pass through single point (focusing)single point (focusing)

http://en.wikipedia.org/wiki/Image:Pinhole-camera.svg

Matthew Clemente; http://en.wikipedia.org/wiki/Image:Pinhole_hydrant_neg_pos.jpg

The Pupil is an ApertureThe Pupil is an Aperture

Pupil Pupil Opening in the center of Opening in the center of

the eyeballthe eyeball Bounded by the Bounded by the IrisIris

The iris controls the size of The iris controls the size of the pupilthe pupil

Opening through which Opening through which light enters the eye light enters the eye

PupilPupil

IrisIris

Petr Novák, Wikipedia http://en.wikipedia.org/wiki/Image:Eye_iris.jpg

Image Formation: AperturesImage Formation: Apertures

To achieve a clear image on To achieve a clear image on an image screen, the an image screen, the aperture must be very smallaperture must be very small

Problems:Problems: Smaller aperture:Smaller aperture:

Fewer photons get throughFewer photons get through Dimmer image Dimmer image

Diffraction and Vignetting Diffraction and Vignetting become significantbecome significant

Image size is largeImage size is large

Solution??Solution??

Small Aperture

Large Aperture

DiffractionDiffraction

Apparent spreading out of waves past small Apparent spreading out of waves past small openingsopenings

http://en.wikipedia.org/wiki/File:Wave_Diffraction_4Lambda_Slit.png

http://en.wikipedia.org/wiki/File:Diffraction1.png

Single Slit Diffraction Pattern

Diffraction by a small apertureDiffraction by a small aperture

1.0

0.0

http://en.wikipedia.org/wiki/File:Airy-pattern.svg

VignettingVignetting Reduction of an image’s brightness at the periphery Reduction of an image’s brightness at the periphery

compared to the centercompared to the center Due to optical elements shading elements behind them, Due to optical elements shading elements behind them,

reducing the effective aperture reducing the effective aperture

David Ball, 2007

http://en.wikipedia.org/wiki/File:Backlight-wedding.jpg

Lenses are the Solution to the Lenses are the Solution to the Aperture ProblemsAperture Problems

Lenses move the focus Lenses move the focus of the light waves past of the light waves past the aperturethe aperture Focuses the image on the Focuses the image on the

screenscreen Allows for Allows for

wider apertureswider apertures Produces Produces

smaller imagessmaller images

Large Aperture Problem

Aperture & Lens SolutionModified from:http://en.wikipedia.org/wiki/Image:Lens3.svg

Lenses of the EyeLenses of the Eye


Lenses of the EyeLenses of the Eye

Cornea Cornea Crystalline LensCrystalline Lens

Primary function = focus the image on the back Primary function = focus the image on the back of the retinaof the retina


Focus

RefractionRefraction Bending of the path of a light wave as it passes Bending of the path of a light wave as it passes

across the boundary separating two mediaacross the boundary separating two media Cause:Cause:

Change in the speed of the light waveChange in the speed of the light wave No change in speed = no refraction!No change in speed = no refraction!

Material A (fast)

Material B (slow)

Optical DensityOptical Density

Optical density of a material determines the Optical density of a material determines the speed of a wave passing through itspeed of a wave passing through it

↑ ↑ Optical density = ↓ Speed Optical density = ↓ Speed

How to remember this conceptHow to remember this concept Water is more dense than airWater is more dense than air Harder to push yourself through water than air Harder to push yourself through water than air

Think of walking on ground (through air) versus in a pool Think of walking on ground (through air) versus in a pool (through water)(through water)

Harder, so you slow down Harder, so you slow down

Index of RefractionIndex of Refraction

Abbreviated as “n”Abbreviated as “n” Indicator of optical Indicator of optical

densitydensity Indicates the number of Indicates the number of

times slower that a light times slower that a light wave would move wave would move through that material through that material than it would in a than it would in a vacuum. vacuum.

MaterialMaterial Index of Index of Refraction Refraction

VacuumVacuum 1.00001.0000

AirAir 1.00031.0003

IceIce 1.311.31

WaterWater 1.331.33

Crown GlassCrown Glass 1.521.52

Flint GlassFlint Glass 1.58-1.661.58-1.66

DiamondDiamond 2.4172.417

Refraction: What direction?Refraction: What direction?

FST = FST = FFast to ast to SSlow, low, TTowards Normalowards Normal Low optical density, low n Low optical density, low n

toto

high optical density, high nhigh optical density, high n Light ray bends Light ray bends

TOWARDS normalTOWARDS normal SFA = SFA = SSlow to low to FFast, ast,

AAway from Normalway from Normal High n to low nHigh n to low n Light ray bends AWAY Light ray bends AWAY

from normalfrom normalPhysics Classroom Tutorial: Refraction and the Ray Model of Lighthttp://www.ddart.net/science/physics/physics_tutorial/Class/refrn/U14L1c.html

Marching Soldiers Analogy

Incidence at non-perpendicular angle to boundary

Refraction: What direction?Refraction: What direction?

What happens if you What happens if you approach perpendicular approach perpendicular to the boundary??to the boundary?? NO refraction!NO refraction! Light must approach the Light must approach the

boundary at an angle for boundary at an angle for refraction to occur.refraction to occur.

Physics Classroom Tutorial: Refraction and the Ray Model of Lighthttp://www.ddart.net/science/physics/physics_tutorial/Class/refrn/U14L1c.html

Marching Soldiers Analogy

Incidence at perpendicular angle to boundary

Refraction: How Much? Refraction: How Much? Snell’s LawSnell’s Law

Quantitative answer to the Quantitative answer to the question of “By how much question of “By how much does the light ray refract?”does the light ray refract?”

nnii*sine(*sine(θθii) = n) = nrr*sine(*sine(θθrr)) nn ii = index of refraction of = index of refraction of

incident mediaincident media nnrr = index of refraction of = index of refraction of

refractive mediumrefractive medium θθ ii = angle of incidence = angle of incidence θθrr = angle of refraction = angle of refraction **Angles are measured from **Angles are measured from

normalnormal Greater the difference in n’s, the greater the difference in Greater the difference in n’s, the greater the difference in angle of incidence and refraction (= more bending)angle of incidence and refraction (= more bending) If nIf nii = n = nrr, then no refraction!!, then no refraction!!

Normal

Θi

Θr

Material A ni

Material B nr

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

Focusing by LensesFocusing by Lenses

Essentially a two boundary systemEssentially a two boundary system

http://en.wikipedia.org/wiki/File:Lens2a.png

Converging LensesConverging Lenses

http://en.wikipedia.org/wiki/File:Lens1.svg

Diverging LensDiverging Lens

http://en.wikipedia.org/wiki/File:Lens1b.svg

Focusing by LensesFocusing by Lenses Focal length (f)Focal length (f)

Quantification of the amount by Quantification of the amount by which light is bent by the lens which light is bent by the lens

Equal to the distance at which the Equal to the distance at which the outgoing light rays intersect (focal outgoing light rays intersect (focal point) when the incoming light rays point) when the incoming light rays are parallel are parallel

Measured in metersMeasured in meters By convention:By convention:

Converging lenses = positive focal Converging lenses = positive focal lengthlength

Diverging lenses = negative focal Diverging lenses = negative focal lengthlength

Determined by:Determined by: Curvature of the lensCurvature of the lens Relative difference in indexes of Relative difference in indexes of

refraction refraction http://en.wikipedia.org/wiki/File:Lens1b.svg

http://en.wikipedia.org/wiki/File:Lens1.svg

Refractive Power of LensesRefractive Power of Lenses

““focusing power of lens”focusing power of lens” Measured in Diopters (D)Measured in Diopters (D) Power (D) = 1 m/fPower (D) = 1 m/f

f = focal length (meters)f = focal length (meters)

Lenses of the Eye: Refractive Power Lenses of the Eye: Refractive Power

CorneaCornea Crystalline LensCrystalline Lens

Focus

Vitreous humor, n = 1.336Crystalline Lens, n = 1.406Aqueous humor, n = 1.336Cornea, n = 1.376Air, n = 1.000

Lenses of the Eye: Refractive Power Lenses of the Eye: Refractive Power CorneaCornea

2/3 total focusing power (39 - 48 diopters)2/3 total focusing power (39 - 48 diopters) Crystalline Lens Crystalline Lens

1/3 focusing power (15 - 24 diopters)1/3 focusing power (15 - 24 diopters)

Focus


Object-Image RelationshipObject-Image Relationship

Image location changes depending on object Image location changes depending on object distance for a given lens’ focal lengthdistance for a given lens’ focal length

The Lens EquationThe Lens Equation 1/f = 1/d1/f = 1/dobjectobject + 1/d + 1/d imageimage

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 f2f

ProblemProblem

Retina is a fixed distance from the cornea-lens Retina is a fixed distance from the cornea-lens system (~22 mm or 2.2 cm)system (~22 mm or 2.2 cm)

Lens EquationLens Equation 1/f = 1/d1/f = 1/dobjectobject + 1/d + 1/d imageimage

In the eye, In the eye, dd imageimage is fixed = distance between cornea lens system and is fixed = distance between cornea lens system and

the retinathe retina ddobjectobject is fixed = distance between the eye and the object is fixed = distance between the eye and the object

being viewedbeing viewed

Solution??Solution??

The Solution is AccomodationThe Solution is Accomodation

AccomodationAccomodation The ability of the eye to The ability of the eye to

change its focal length (f)change its focal length (f) Mediated by the lens and Mediated by the lens and

ciliary musclesciliary muscles http://en.wikipedia.org/wiki/Eye

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

AccomodationAccomodation

Viewing Nearby ObjectsViewing Nearby Objects Ciliary muscles contract Ciliary muscles contract

Squeeze the lens into a more Squeeze the lens into a more convex (fat) shapeconvex (fat) shape

Pushes cornea bulge out Pushes cornea bulge out further = greater curvaturefurther = greater curvature

C-L system has a short C-L system has a short focal lengthfocal length High refractive powerHigh refractive power

Viewing Distant ObjectsViewing Distant Objects Ciliary muscles relaxedCiliary muscles relaxed

Lens assumes a flatter Lens assumes a flatter (skinnier) shape(skinnier) shape

Cornea is not pushed Cornea is not pushed out = less curvatureout = less curvature

C-L system has a C-L system has a long focal lengthlong focal length Low refractive Power Low refractive Power

Erin Silversmith, AzaToth http://en.wikipedia.org/wiki/Image:Focus_in_an_eye.svg

Far PointFar Point

Farthest point at which an object can be brought Farthest point at which an object can be brought into focus by the eyeinto focus by the eye

Typically is infinityTypically is infinity Decreases with ageDecreases with age

Near PointNear Point

Closest point at which an object can be brought Closest point at which an object can be brought into focus by the eyeinto focus by the eye Ideally ~25 cmIdeally ~25 cm

Finger ExperimentFinger Experiment Limited by the curvature of the cornea and Limited by the curvature of the cornea and

adjustable radii of the lensadjustable radii of the lens Recedes with age (can lead to farsightedness)Recedes with age (can lead to farsightedness)

The Power of AccomodationThe Power of Accomodation

What is the maximum change in focusing power due to What is the maximum change in focusing power due to accomodation for a typical eye?accomodation for a typical eye?

PPaccomodationaccomodation = P = Pfar pointfar point - P - Pnear pointnear point

P = 1/fP = 1/f 1/f = 1/d1/f = 1/dobjectobject + 1/d + 1/d imageimage

Assume image distance (lens to retina) = 2 cmAssume image distance (lens to retina) = 2 cm 1/f1/ffar pointfar point = 1/d = 1/dobjectobject + 1/d + 1/d imageimage

PPfar pointfar point = 1/infinity + 1/0.02 = 0 + 50 = 50 D = 1/infinity + 1/0.02 = 0 + 50 = 50 D

1/f1/fnear pointnear point = 1/d = 1/dobjectobject + 1/d + 1/d imageimage

PPnear pointnear point = 1/0.25 + 1/0.02 = 4 + 50 = 54 D = 1/0.25 + 1/0.02 = 4 + 50 = 54 D

PPaccomodationaccomodation = P = Pfar pointfar point - P - Pnear point near point = 50 D – 54 D = 4 D= 50 D – 54 D = 4 D

Visual Defects and CorrectionVisual Defects and Correction

Visual defectsVisual defects When an eye cannot focus an obect’s image on the retinaWhen an eye cannot focus an obect’s image on the retina

Image formed in front of or behind the retinaImage formed in front of or behind the retina Results in blurred visionResults in blurred vision

Typical causes:Typical causes: Abnormal length of the eyeball Abnormal length of the eyeball Abnormal curvature of the corneaAbnormal curvature of the cornea Abnormal accomodationAbnormal accomodation

CorrectionCorrection Glasses or Contact lensesGlasses or Contact lenses

Hyperopia (Farsightedness)Hyperopia (Farsightedness)

INABILITY of the eye to focus on NEARBY objectsINABILITY of the eye to focus on NEARBY objects ““Can see far” – no difficulty focusing on distant objectsCan see far” – no difficulty focusing on distant objects Images of nearby objects are formed at a location Images of nearby objects are formed at a location

BEHIND the retinaBEHIND the retina Near point is located farther away from the eyeNear point is located farther away from the eye

Hyperopia: CausesHyperopia: Causes

Shortened eyeball (retina is closer than normal to the cornea lens Shortened eyeball (retina is closer than normal to the cornea lens system)system) Axial hyperopiaAxial hyperopia

Cornea is too flatCornea is too flat Refractive hyperopiaRefractive hyperopia

Lens can not assume a highly convex (fat) shapeLens can not assume a highly convex (fat) shape Refractive hyperopiaRefractive hyperopia

Hyperopia: CorrectionHyperopia: Correction

Need to refocus the image on the retinaNeed to refocus the image on the retina Decrease the focal length of the cornea-lens systemDecrease the focal length of the cornea-lens system

Add a converging lens (positive power, +D)Add a converging lens (positive power, +D)

PresbyopiaPresbyopia

““After – 40” vision After – 40” vision Progressively diminished ability to focus on near Progressively diminished ability to focus on near

objects as one agesobjects as one ages Similar to hyperopia, but different causeSimilar to hyperopia, but different cause Type of refractive hyperopiaType of refractive hyperopia

Cause = diminished power of accomodation due to Cause = diminished power of accomodation due to natural process of agingnatural process of aging Reduced elasticity of the lens Reduced elasticity of the lens Weakening of the ciliary musclesWeakening of the ciliary muscles Changes in lens curvature due to Changes in lens curvature due to

continued growthcontinued growth

http://en.wikipedia.org/wiki/Image:Specrx-accom.png

Myopia (Nearsightedness)Myopia (Nearsightedness)

Inability of the eye to focus on DISTANT objectsInability of the eye to focus on DISTANT objects ““Can see near” – no difficulty focusing on nearby Can see near” – no difficulty focusing on nearby

objectsobjects Images of distant objects are formed in front of the Images of distant objects are formed in front of the

retinaretina Far point is closer than normalFar point is closer than normal

Causes of MyopiaCauses of Myopia

Not usually caused by agingNot usually caused by aging Elongated eyeball (retina is farther away than normal Elongated eyeball (retina is farther away than normal

from the cornea-lens system)from the cornea-lens system) Axial myopiaAxial myopia

Bulging cornea (greater curvature)Bulging cornea (greater curvature) Refractive myopiaRefractive myopia

Correction of MyopiaCorrection of Myopia

Need to refocus the image on the retinaNeed to refocus the image on the retina Increase the focal length of the cornea-lens systemIncrease the focal length of the cornea-lens system

Add a diverging lens (negative power, -D)Add a diverging lens (negative power, -D)

AstigmatismAstigmatism

Most common refractive errorMost common refractive error Blurred or sometimes distorted vision at any Blurred or sometimes distorted vision at any

distancedistance Cause: Cause:

Irregularly shaped cornea or lensIrregularly shaped cornea or lens More oblong than spherical More oblong than spherical Refractive power differs between regionsRefractive power differs between regions

CorrectionCorrection Glasses Glasses

Lenses with different radii of curvature in different planesLenses with different radii of curvature in different planes

Power of Corrective EyewearPower of Corrective Eyewear What is the strength of lens needed to correct a myopic eye that What is the strength of lens needed to correct a myopic eye that

has a far point of 2.0 m?has a far point of 2.0 m? PPcorrectivecorrective = P = Pdesireddesired - P - Pactualactual


Assume image distance (lens to retina) = 2 cmAssume image distance (lens to retina) = 2 cm Desired:Desired:

1/f1/fdesired far pointdesired far point = 1/d = 1/dobjectobject + 1/d + 1/d imageimage

PPdesired far pointdesired far point = 1/infinity + 1/0.02 = 0 + 50 = 50 D = 1/infinity + 1/0.02 = 0 + 50 = 50 D Actual:Actual:

1/f1/factual far pointactual far point = 1/d = 1/dobjectobject + 1/d + 1/d imageimage

PPactual far pointactual far point = 1/2 + 1/0.02 = 0.5 + 50 = 50.5 D = 1/2 + 1/0.02 = 0.5 + 50 = 50.5 D

PPcorrectivecorrective = P = Pdesireddesired - P - Pactual actual = 50 D – 50.5 D = -0.5 D= 50 D – 50.5 D = -0.5 D

**Check Sign of corrective power (Does it make sense?)**Check Sign of corrective power (Does it make sense?)

DiffractionDiffraction

Apparent spreading out of waves past small Apparent spreading out of waves past small openingsopenings

http://en.wikipedia.org/wiki/File:Wave_Diffraction_4Lambda_Slit.png

http://en.wikipedia.org/wiki/File:Diffraction1.png

Single Slit Diffraction Pattern

Diffraction by a small apertureDiffraction by a small aperture

1.0

0.0

http://en.wikipedia.org/wiki/File:Airy-pattern.svg

More info or clarificationMore info or clarification

[email protected]@utah.edu The Physics Classroom Tutorial The Physics Classroom Tutorial

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/BBoard.htmlhttp://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/BBoard.html

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/BBoard.html

Review QuestionsReview Questions

Lecture 1: OpticsLecture 1: Optics

Question # 1Question # 1

Question: What is the eye?Question: What is the eye?A. A sensory organ mediating the sense of sightA. A sensory organ mediating the sense of sight

B. A structure that detects light and converts it into B. A structure that detects light and converts it into neural responses that the brain interpretsneural responses that the brain interprets

C. A structure whose anatomy is designed to focus C. A structure whose anatomy is designed to focus light rays so that an image is formed on the back of light rays so that an image is formed on the back of the retinathe retina

D. All of the aboveD. All of the above

Answer: D. Answer: D. All of the above All of the above


Question: Converging lenses of the eyeQuestion: Converging lenses of the eyeA. Include the cornea and crystalline lensA. Include the cornea and crystalline lensB. Include the cornea and pupilB. Include the cornea and pupilC. Refract light rays to focus the image on the back of the C. Refract light rays to focus the image on the back of the

retinaretinaD. Both A and BD. Both A and BE. Both A and CE. Both A and C

Answer: E.Answer: E. The cornea and crystalline lens are the two lenses of the eye. 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 The pupil is an aperture, not a lens, which allows light rays to pass through but does not refract them. The cornea-lens pass through but does not refract them. The cornea-lens system refracts (bends) incident light rays to focus the image system refracts (bends) incident light rays to focus the image on the back of the retinaon the back of the retina


Question: Under what circumstances will refraction Question: Under what circumstances will refraction occur?occur?

A. When a light ray passes across any boundary A. When a light ray passes across any boundary

B. When a light ray approaches at an angle to a 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 C. When a light ray changes speed due to entrance into a material of a different optical densitymaterial of a different optical density

D. A and BD. A and B

E. B and CE. B and C

F. All of the aboveF. All of the above

Answer: E. Answer: E. Both B and C are true. Both B and C are true.


Question: What is the direction of refraction if the light wave Question: What is the direction of refraction if the light wave crosses a boundary from a material with a high index of crosses a boundary from a material with a high index of refraction (high n) into a material with a low index of refraction (high n) into a material with a low index of refraction (low n)?refraction (low n)?

A. Towards normalA. Towards normalB. Away from normalB. Away from normal

Answer: B. Answer: B. Solution: Solution: high n = high optical density = slowhigh n = high optical density = slow

low n = low optical density = fastlow n = low optical density = fastIf going from large n to small n, then going from If going from large n to small n, then going from

slow to fast mediumslow to fast mediumSFA = if go from SFA = if go from SSlow to low to FFast, then bend ast, then bend AAway way

from normalfrom normal


Question: You have created a new kind of plastic that is Question: You have created a new kind of plastic that is highly transparent and very resistant to scratching. It highly transparent and very resistant to scratching. It would make an excellent material for use in eye glasses. would make an excellent material for use in eye glasses. So, you need to know what the index of refraction is for So, you need to know what the index of refraction is for this new material. You set up a simple experiment in this new material. You set up a simple experiment in which you measure the angles of incidence and refraction which you measure the angles of incidence and refraction of a laser light as it passes from air (index of refraction is of a laser light as it passes from air (index of refraction is known) into the new plastic. What equation would you known) into the new plastic. What equation would you use to determine the index of refraction of your new use to determine the index of refraction of your new plastic?plastic?A. Lens EquationA. Lens EquationB. Snell’s LawB. Snell’s LawC. Angle EquationC. Angle EquationD. Refraction LawD. Refraction Law

Answer: A. Snell’s LawAnswer: A. Snell’s Law

Air (“n” = 1.0003)

New Plastic (“n” = ?)

60°

35°

Question # 6Question # 6Question: Consider the phenomenon of accomodation. Under what Question: Consider the phenomenon of accomodation. Under what

condition do the ciliary muscles have to do the most work?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 A. When shortening the focal length of the cornea-lens system to view far

off objectsoff objectsB. When lengthening the focal length of the cornea-lens system to view far B. When lengthening the focal length of the cornea-lens system to view far

off objectsoff objectsC. When shortening the focal length of the cornea-lens system to view C. When shortening the focal length of the cornea-lens system to view

objects that are near.objects that are near.D. When lengthening the focal length of the cornea-lens system to view D. When lengthening the focal length of the cornea-lens system to view

objects that are near. objects that are near.

Answer: C.Answer: C. The focal length of the cornea lens system must be shortened to focus the image of a 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 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 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 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 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 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 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.when the ciliary muscles are relaxed during viewing of far off objects.


Question: If you took a fish out of water, would it exhibit Question: If you took a fish out of water, would it exhibit hyperopia or myopia when trying to see in air?hyperopia or myopia when trying to see in air?

A. HyperopiaA. HyperopiaB. MyopiaB. Myopia

Answer: B. Answer: B. Water has an index of refraction of 1.33Water has an index of refraction of 1.33 Air has an index of refraction of 1.0003Air has an index of refraction of 1.0003 The index of refraction of the cornea-lens system is 1.37-1.4The index of refraction of the cornea-lens system is 1.37-1.4 Both situations have light traveling from fast to slow so light Both situations have light traveling from fast to slow so light

rays will bend the same direction in both situations.rays will bend the same direction in both situations. Going from air to the eye is a greater change in the index of Going from air to the eye is a greater change in the index of

refraction = greater change in angle of refractionrefraction = greater change in angle of refraction So image would form in front of the retina = MyopiaSo image would form in front of the retina = Myopia

Focus


Water, n = 1.333


Question: Question: How does an optometrist correct for hyperopia?How does an optometrist correct for hyperopia?

A. Equips the eye with a diverging lens to shorten the focal length of the cornea-A. Equips the eye with a diverging lens to shorten the focal length of the cornea-lens systemlens system

B. Equips the eye with a diverging lens to lengthen the focal length of the cornea-B. Equips the eye with a diverging lens to lengthen the focal length of the cornea-lens systemlens system

C. Equips the eye with a converging lens to shorten the focal length of the cornea-C. Equips the eye with a converging lens to shorten the focal length of the cornea-lens systemlens system

D. Equips the eye with a converging lens to lengthen the focal length of the cornea-D. Equips the eye with a converging lens to lengthen the focal length of the cornea-lens systemlens system

Answer: C.Answer: C. Hyperopia (farsightedness) occurs when the eye cannot focus on nearby objects because their 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 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 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.rays and so a converging lens is added in front of the cornea lens system.

Power of Corrective EyewearPower of Corrective Eyewear What is the strength of lens needed to correct a myopic eye that What is the strength of lens needed to correct a myopic eye that

has a far point of 2.0 m?has a far point of 2.0 m? PPcorrectivecorrective = P = Pdesireddesired - P - Pactualactual


Assume image distance (lens to retina) = 2 cmAssume image distance (lens to retina) = 2 cm Desired:Desired:

1/f1/fdesired far pointdesired far point = 1/d = 1/dobjectobject + 1/d + 1/d imageimage

PPdesired far pointdesired far point = 1/infinity + 1/0.02 = 0 + 50 = 50 D = 1/infinity + 1/0.02 = 0 + 50 = 50 D Actual:Actual:

1/f1/factual far pointactual far point = 1/d = 1/dobjectobject + 1/d + 1/d imageimage

PPactual far pointactual far point = 1/2 + 1/0.02 = 0.5 + 50 = 50.5 D = 1/2 + 1/0.02 = 0.5 + 50 = 50.5 D

PPcorrectivecorrective = P = Pdesireddesired - P - Pactual actual = 50 D – 50.5 D = -0.5 D= 50 D – 50.5 D = -0.5 D

**Check Sign of corrective power (Does it make sense?)**Check Sign of corrective power (Does it make sense?)

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

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