Physics of the Eye

8/2/2019 Physics of the Eye

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Lens Maker Equation

1 2

1 1 1( 1)( )n

f R R

Thin Lenses in Contact

1 2

1 1 1

f f f

R and f are + if convex, - if concave.


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Examples:

1. A plano-convex lens is made of glass of

index of refraction equal to 1.5. The curvedsurface has a radius of 20cm. What is thefocal length of the lens?

2. A double concave lens is made of glass(n=1.5) and has a focal length of 30cm. Ifthe radius of one of the surfaces is 30cm,find the radius of the other surface.

3. What is the resulting focal length and power iftwo thin lenses each of focal length +25cmare in contact?


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4. An object 0.3m from a lens gives a virtual

image 0.1m from the lens. What is the focallength and nature of the lens?

5. The focal length of a lens is 5cm. How far

must the lens be adjusted from the screen toproduce a clear image of a) an object that 2maway b) a distant object?

6. How far from a converging lens (f =15cm)must an object be placed in order to producean image that is a) inverted and magnified

three times b) upright and magnified threetimes?


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7.A converging lens has a focal length of8cm. An object is located 14.0cm in front

of this lens. A second converging lens ofthe same focal length is located 20cm tothe right of the first lens. Relative to thesecond lens, where is the final image?

Obtain over all magnification.

8. A converging lens (f=12cm) is located30cm to the left of a diverging lens 9f=-

6.0cm). An object is located 36cm to theleft of the converging lens. Locate the finalimage relative to the diverging lens.


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The Physics of the Eye

The eye is an opaque ball averaging 2.3cm in diameter


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Parts of the Eye


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Cornea- outer thin transparent membraneof the eyeball. The cornea serves to protectthe eye and refract most of the incident light.

Pupil-The black circle that we see in themiddle of the eye. The pupil is actually anopening through light enters the inner portion

of the eye. It changes its size to regulateamount of light entering the eye.


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Iris- the colored circle of the eye.

It may be brown, black, gray and othersdepending on race.

Its main task is to regulate the size of the

pupil by contraction or relaxation of itsmuscles.

It has been claimed that each iris is unique

and is a better identifier than thefingerprints


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Trivia:. Iridology is the study of the iris ofthe eye. The iris is divided into 40 zones,each corresponding to different body parts

and that diseases of different body partsmay be diagnosed by mere looking at theiris.

Ignatz Von Peczely(1866)father ofiridology.


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Sclera-The white background of theeye. It provides structure, protection andstrength to the eye.

Crystalline lensclear convex structure atthe back of pupil. It can focus objects aredifferent distances by changing its shape.

This ability of the lens is calledaccommodation.


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The ciliary muscles are attached to thecrystalline lens and are responsible forchanging the shape of the lens when

focusing objects at different distances. Tofocus on a nearby object, the musclescontract and the center of the lens are

thicker. If the object is distant, the musclesare relaxed and the lens is thin.


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ACCOMMODATION


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Retina

1. For normal vision, the image of anobject seen by the eye is formed exactly at

the retina.2. The retina consists of light sensitiverods and cones. The cones can distinguish

color and are responsible for our daytimevision. On the other hand, the rods enableus to see in the dark


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Fovea- the region of most distinct vision.

There are about 200,000 cones but norods in the fovea.

Blind Spot-the point in the retina where the

optic nerves exit is called the blind spot. The optic nerve carries images from the

retina to the brain.


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The Blind Spot Experiment

Close your left eye and look at the figures in this box with your right eye only.You can see both the square and the circle. Try moving this book slowlytowards your face. You will reach a certain distance where the circledisappears. Does the same thing happen when you repeat the procedureusing the left eye?


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aqueous humor located between thecornea and lens

vitreous humorlocated after the lens

Both humors are responsible for giovingthe eye its near perfect spherical shape.

They also belong to the refractive systemof the eye.


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Do you know that your eyes revealyour emotions?


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20/20 vision

Visual acuity simply means clarity of visionor sharpness of vision.

It is expressed usually as a fraction. The

numerator is the standard testing distance, 20feet in almost all countries and 6meters inBritain. The denominator represents thedistance in feet or meters at which a person with

normal vision is able to see clearly an objectseen by another at 20 feet or 6meters.


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If your vision is 20/50, you can see at 20 ftwhat a normal vision man can see at 50 ft.Hawks for instance have 20/2 vision.

Legal blindness is usually defined asvisual acuity less than 20/200 withcorrective lenses


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VISUAL ACUITY


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EYE DEFECTS

The closest distance at which an objectcan be seen clearly by the eye is calledthe near point of the eye. The near point

for young adults with normal vision is 25cm, for children around 10 cm and for theaged, 50 cm or more.


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(www.main.com/~gj/physics/anna/)LEONARDO DA VINCIWhile it is true that hismasterpieces like Mona Lisa,

Madonna of the Rocks and

The Last Supper have broughthim fame, his many sketchesand notes have been the basisof modern scientific inventions.He was the originator of theconcept of contact lens. In

1508, he sketched anddescribed several forms ofcontact lenses though notproducing even one for testing.


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The far point of the eye is the farthestdistance at which an object can beseen clearly. The far point of the normal

eye is taken as infinity.

Thus, a normal healthy eye can seeobjects as close as 25cm or very distant

from it.


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Myopiais the medical term fornearsightedness. People suffering from

this visual problem can see close objectsclearly but the distant ones are blurred.

A myopic eye forms the image of a distant

object in front of the retina because theeyeball is longer than the normal or toocurved.

This can be corrected by using a diverginglens.


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The far point of a person is 2.0m away ratherthan infinity. What corrective lens should beprescribed? What should be the power of thislens?

A persons right eye is corrected by a 4.0Dlens, worn 1.8 cm from the eye. A) Is the personnearsighted or farsighted? B) What is thispersons near point without glasses? C) What ishis far point without glasses? D) Suppose hedecided to use contact lens instead ofeyeglasses, what should be the power of thecorresponding contact lens?


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A person suffering from hypermetropia(hyperopiain some books) orfarsightedness can see distant objects but

can not focus clearly on nearby objects. Inthis case, the eyeball is too short and theimage of a close object is formed behind

the retina. A converging lens can correctthis problem.


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A farsighted person has a near pointlocated 210cm from the eyes. Determinethe power of the lens to be used.


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People aged 40 and above are suffering frompresbyopia. Presbyopiais sometimes called theaging eyes or old eyes in as much as it is a normalconsequence of growing old and cannot beprevented. As we grow old, the crystalline lens hardensand the ciliary muscles become less flexible makingaccommodation not as easy as before. As a result ofthis, distant objects are seen clearly, but nearby objects

are not. We see elderly people holding a newspaper atarms length to read it. A presbyopic eye needs readingglasses. Alternatively, a bifocal lens may be prescribed.The upper half of a bifocal lens is for normal viewingwhile the lower half is for reading purposes. A lineseparates the upper from the lower half. A bifocal lensproduces the so called split- image effect and revealsthe age of the user. To eliminate these, a no-line bifocallens or progressive lens may be used.


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A person suffering from astigmatismcannot focus simultaneously on horizontaland vertical lines. The corneas having

unequal curvature in various directionscauses this. A cylindrical lens is used tocorrect astigmatism.


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Pinhole Glasses

Introduced in 1995, pinhole glasses or stenopeicglasses are not made of glasses but of opaquematerial containing holes about 1.0mm in

diameter. Pinhole glasses are said to correctrefractive errors by admitting only those rays that

pass through the central portion of the pupil .


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Laser vision surgery has been a popularprocedure to correct eye defects. PRK

(Photorefractive Keratectomy) and LASIK (LaserAssisted in-situ Keratomileusis) use the excimerlaser to reshape the cornea so that images areformed at the retina. The procedures takeapproximately 10 minutes, with actual laser time

exposure varying from 15 to 60 seconds. Peoplewho have undergone this surgery feel no painbut may experience a foreign body sensationlasting for several hours (LASIK) and 3 to 4 days(PRK).


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LASIKLaser Assisted In-Situ Keratomileusis


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Bionic Eye

It comprises a computer chip thatsits in the back of the individual'seye, linked up to a mini videocamera built into glasses that theywear.Images captured by the camera

are beamed to the chip, whichtranslates them into impulses thatthe brain can interpret


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COMPARISON BETWEEN EYE AND CAMERA

EYE CAMERA

1. Opening for light to

enterPupil Aperture

2. Regulation of size ofopening

Muscles of the iris Diaphragm

3. Refracting system Cornea, lens, vitreous

and aqueous humorBiconvex lens

4. Where image isformed

Retina Film

5. Regulation of time ofexposure to light

eyelid shutter

6. Focusing mechanism Ciliary muscles change

the shape of lens


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Digital Camera

A digital camera captures the image through asensor composed of array of electrodes orphotosites. The image sensor can be a chargecoupled device (CCD) or complementary metal

oxide semiconductor (CMOS). The sensorconverts light to electrical signals. The signalsare converted into binary number by means ofan analog to digital converter, processed by abuilt in computer and stored in a memory card in

JPEG or TIFF format. The first consumer-oriented digital cameras

were sold by Kodak and Apple in 1994.


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CMOS image sensor( Source: How StuffWorks)

Both CCD and CMOS image sensors convert light into electrons

CCD sensor (Source: HowStuff Works)


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Magnifier and CompoundMicroscope

A magnifying glass is simply aconverging lens that produces a virtual,upright and enlarged image of an

object placed at a distance less than itsfocal length.


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The angular magnification M of a magnifieris defined as the ratio of the angular sizeof the image it produces to the angular

size of the object placed at the near pointand viewed by a naked eye.


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ph

phM

cm25

cm25/

/

tan

'tan'


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But 1/p = 1/f 1/di. Since the image formed bythe magnifying glass is virtual, the imagedistance q must be negative. Thus, 1/p = 1/f +1/di. Substituting this in the equation forangular magnification

idfM

11cm25

Both f and q must be in centimeters.


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If the object is viewed at a distance equal tothe focal length, the image is formed at infinity.

fM

cm25


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For an image formed at 25cm,

1cm25

fM

*A short focused lens produces greater magnification thanlong focused lens.

*Antoni Van Leeuwenhoek,the father of microbiology, issaid to have produced a magnifying glass from glassbead with a magnification of 275.


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A biologist examines a specimen using asimple magnifier of power 12D. What isthe angular magnification if the final image

is produced at a) infinity b) at the normalnear point of the eye?


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Compound Microscope

Magnifying glass with an additional lens. Objective-

* lens near the object to be viewed,

* pre-magnifies the object by producinga real, inverted and enlarged image.This image becomes the object for the

eyepiece.


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Eyepiece-

* magnifying glass, lens near the eye

*produces an enlarged, virtual and uprightfinal image.

The compound microscope was believed to beinvented by the father and son team of Hans andZacharias Jannsen in 1590


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To obtain large magnification, the object is placed at adistance approximately equal to the focal length of theobjective (fo).

Also, compound microscopes are designed so that theeye is fully relaxed when viewing the final image. Anecessary condition for this is that the final image mustbe very far from the eyepiece or at infinity. This will only

be true if the first image formed by the objective fall justinside the focal point of the eyepiece. If the objectiveand the eyepiece were separated by a distance L, itfollows that the distance of the first image from theobjective is L fE, where fE is the focal length of the

eyepiece. The magnification produce by the objectiveand the eyepiece are respectively


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Magnification by a Compound Microscope

Eo E

o E

andL fq 25

M Mp f f

Final Magnification M

E

o E

o E

L fM M M 25

f f

Greater magnification is achieved by using short focusedobjective and eyepiece lenses.


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Antoni van Leeuwenhoeks simple microscope. The object being

examined was fixed to the spike and viewed through a singleconverging lens. (Source: Grolier International Encyclopedia)


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Telescope

A telescope is device that enables us to seedistant object. There are two types of telescope:refracting and reflecting telescope.

A refracting telescope makes use of lenses for

its objective and eyepiece. A reflecting telescopeuses a concave mirror, instead of a converginglens, as the objective.


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History claims that the telescope wasaccidentally invented by a Dutchlensmaker Hans Lippershey in 1608 when

he looked at a distant church using two ofhis converging lenses. He called hisinvention look glass and applied for a

patent. However, he was denied because it was too simple that everyone knows it

during his time.


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Galileos far looker uses a converging

lens for the objective and a diverging lensfor the eyepiece.


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For the objective: object distance is at infinity.Hence thefirst image is formed just beyond the principal focus ofthe objective. This first image is real, inverted and

smaller. For the eyepiece: The image formed by the objective

normally lies just inside the focal point of the eyepiece.The eyepiece, acting like a magnifying glass, produces amagnified virtual final image at infinity.

The distance between the two lenses is therefore thelength of the telescope and is equal to the sum of thefocal lengths of the two lenses.

The angular magnification of the telescope is the ratio of

focal length of the objective to that of the eyepiece.

o

E

fM = -

f


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A physics student was tasked to make atelescope out of old glass lenses havingthese focal lengths: 4.0cm, 8.0cm, 9.0cm,

12.0 cm and 16.0cm. Which combinationwill produce the maximum magnification?What is this maximum magnification?


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Hubble Space Telescope launched on April25, 1990(Source NASA)
http://www.centennialofflight.gov/essay/Dictionary/HST/DI196G1.htm

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Physics of the Eye