61

Optical Instruments

CHAPTE R 6

INTRODUCTION-In the last two chapters we disshycussed devices used for observing the world The earliest such device was of course the eye all you have to do is look The camera allowed you to record an image on film so you could look at it later This chapshyter treats devices that improve the image to be detected These not only allow you to see a better quality image but to see images of objects that you otherwise couldnt see beshycause they are too small too far or too transparent As John Trumbull wrote But optics sharp it needs I weenfro see what is not to be seen

62 SINGLE-LENS INSTRUMENTS-Several op tical instruments use only one lens-the simple camera is an example weve already met Here well see that the simple lens can solve a variety of optical problems

A Eyeglasses spherical correction

Eyeglasses or contact lenses are used to improve the Image on the retina when the lens system of the eye is defective When the ciliary muscles of a normal eye are relaxed (we call It relaxed eye for brevity) its power Is just enough to bring parallel rays from a distant object to a focus on the retina We say that

the far point (the farthest Object that can be clearly seen) of a normal eye is at infinity In order to focus on closer Objects the ciliary musshycles tense to shorten the focal length of the eyelens (accommodashytion) We call the closest point on which an eye can focus the near point For a normal eye this is taken to be 25 cm (This distance actually varies from eye to eye even for eyes in no need of correction To locate your own near pOint hold this page so near that it looks blurred using only one eye Then move the page away until the letters just come back into focus The page is then at the near point for that eye You should try this both with and without your glasses or contact lenses If you wear them)

As the normal eye accommodates between infinity and 25 cm the power of the eyelens changes We can think of the accommodated lens of the eye as being made of two fictitious lenses one of which is the relaxed lens of the eye (focused on infinity) and a second lens that alshylows the eye to focus on a point only 25 cm away The second fictitious lens must then accept rays from a point 25 cm away and convert them to parallel rays so that the first lens can focus them onto the retina Hence the second lens must have a focal length of 25 cm = t m Its power of 4 dlopters adds to that of the first lens (Sec 34EJ so during the process of accommodation the

power of the eye must change by 4 diopters (The actual range of acshycommodation will vary from eye to eye In youth it is as large as 14 diopters corresponding to a near point of 7 cm and it usually deshycreases with age)

Many eyes however do not have the correct power in the relaxed state for the size of the eyeball (Sec 52A) Figure 61 shows all in the relaxed state a normal eye an eye with too much power (myopia) and an eye with too little power (hyshyperopia) all looking at an object loshycated at infinity (parallel incident light) The images on the retinas of the defective eyes are blurred The obvious cure is to put an approprishyate lens in front of each defective eye so as to increase the power of the hyperopic eye or to decrease the power of the myopiC eye If the deshyfective eyes have the normal range of accommodation both the near and the far point of vision will thereby be moved to the normal poshysitions Lets look at the way this is done

Consider first the myopic eye Its power in the relaxed state is already too large and accommodation will only make it larger Therefore the unaided myopic eye will always see distant Objects blurred Its far point

FIGURE 61

Relaxed eyes viewing a distant object (a) normal (b) myopic (c) hyperopic

(a) (b) (c) 159

CHAPTER 6 OPTICAL INSTRUMENTS

160

I ~ I Distance to far point(a)

0 0

I Distance to far point = Focal length (b)

is at some closer distance say at 50 cm (Fig 6 2a) (This close distance would correspond to the power of the eyes compound lens being only 3 too large) If the eyes accomshymodation is normal (4 diopters) its near point is then closer than the normal near point (in this case it turns out to be 17 cm) Thus a myshyopic person has only a relatively small range of distances over which she can see clearly but at the near point she can see a larger more deshytailed image of the object than a normal viewer can at his near point-the myope has a kind of built-In magnifying glass In fact if your eye is normal and you want to know how the world looks to a myshyope you need only look through a magnifying glass held close to your eye Since magnifying glasses were not used as visual aids until the thirteenth century it has been sugshygested that the artisans responsible for the delicate engraving found in jewelry and coins from well before that time were actually myopic Being hereditary this trait as well as the tricks of the engraving trade would have been handed down from one generation of artisans to the next

The cure for a myopic eye is a dishyverging eyeglass whose negative power decreases the eyes excessive power and moves the far point back

FIGURE 62

Relaxed myopic eye (a) without glasses (b) with glasses The diverging lens is drawn separated from the eye to show that the rays leaving the glasses look as in (a) but there need be no separation the correction works also for contact lenses

to infinity where it belongs Altershynatively put it bends parallel rays from distant objects so that they appear to be coming from a virtual image If this image is located at the far point the relaxed myopic eye can see it clearly (see Fig 62b and compare with Fig 323a) Hence the lens must have a focal length equal to the distance to the far point of the relaxed myopic eye For our example where the far point is at 50 cm the proper diverging eyeshyglass has] = -50 cm = - 1 m so the prescription for this lens would read - 2 diopters (The normal eyes compound lens has a power of about 60 diopters when relaxed The myopic eye in this case had the excessive power of 62 diopters the eyeglasses reduce it back to the normal value)

Now consider the hyperopic eye Its power is too small in the relaxed state-suppose it is only 57 diOpshyters This hyperope already has to accommodate (by 3 diopters) to the normal value of 60 diopters in order

to see distant objects (Fig 63a) However the very highest power he can reach by accommodation is 61 diopters Since this is only 1 diopshyter above that necessary to see disshytant objects his near point is at 1 m (see Figs 63b and c) To see objects that close he must use all his accommodation ability thereshyfore he cannot focus on anything closer

The cure for this eye is a convergshying eyeglass that raises the power by 3 diopters to reach the normal 64 diopters when fully accommoshydated That is the prescription would read + 3 diopters Consider the effect of such an eyeglass lens on an object at the normal near point of 25 cm It will make a virshytual image at 1 m where the hypershyopic eye can see it (See Fig 63d and try the construction by ray tracing)

As the accommodated uncorshyrected hyperopic eye can focus on distant objects hyperopic people were once called farsighted Simishylarly the extra strong myopic eye when fully accommodated can foshycus on objects closer than the norshymal 25 cm and was therefore called nearsighted These names howshyever are misleading if the eye cant accommodate properly as often happens as you grow older The agshying process adds flatter layers to the eyelens (see Fig 59) These layers not only reduce the eyelens power (reducing any myopia that may be present) but also separate the inshyner core from the humors that bathe the eyelens This older inner core then tends to become less flexshyible and pliant and the eye does not accommodate as well This condishytion called presbyopia prevents an otherwise normal eye from foshycusing on near Objects In his poem Typical Optical John Upshydike writes

In the days oj my youth mid many a caper

[ drew with my nose a mere inchJrom the paper

but now that Im older and life h as grown hard

[find [ cantJocus inside oj a yard

Greek presbus old man

-

62 SINGLE-LENS INSTRUMENTS

161

(a)

0 bullbull 0shy

0

1---- 25 em - ----gt11 (b)

_------ Distanee to near point-------~

(e)

+Q

~ ~middotf ~1~SJ

-_---r---- D lt0 ~~ ~ (d)

FIGURE 63

The hyperopic eye (a) partially accommodated (b) fully accommodated object at 25 cm (c) fully accommodated object at near point (d) corrected fully accommodated object at 25 em appears to be at near pOint

The aged eye may then require one eyeglass prescription for distant viewing and another for close-up The two lenses are often combined

into a bifocal lens with the closeshyup lens in the lower half of the frame (since you generally look downward toward close objects) Bishyfocals can now be made in which the lenses in the two halves gradushyally fade into one another thus eliminating the conspicuous line across the lens

Convex lenses for the hyperopic eye were in use at the end of the thirteenth century but it was a

century and a half later before conshycave lenses appeared for the more common myopic eye It was another century or so before anybody undershystood how these lenses worked to assist the eye

B Eyeglasses cylindrical correction

Another common eye defect astigshymatism occurs when the cornea is not spherical but is more curved in one plane than in another That is the focal length of the astigmatic eye is different for rays in one plane than for those in a perpendicular plane It cannot for example focus simultaneously on both the horishyzontal and vertical glazing bars of a window Figure 64 provides a sim-

FIGURE 64

Test for astigmatism Close one eye and view this figure through the other eye (without glasses or contact lenses) Hold the figure sufficiently close to the eye so that all lines look blurred Then gradually move the figure away until one set of lines comes into focus with the rest blurred (If two adjacent sets come into focus together rotate the figure a little until only one is in focus If all sets come into focus together you don t have astigmatism ) You have now found the near pOint for a line in the direction of the lines that are in focus Move the pattern away further until the lines perpendicular to the first set come into focus (The first set mayor may not remain in focus) This is the near po int for a line perpendicular to the o riginal set The different near points mean that your eye has a different focal length for lines parallel to and perpendicular to the original set Try the procedure again with your glasses or contact lenses to see if your astigmatism is corrected

CHAPTER 6 OPTICAL INSTRUMENTS

162

pie test for astigmatism in your eyes (The difference in focal length in the defect astigmatism occurs all over the field of view it should not be confused with the off-axis abershyration astigmatism Sec 3 5D )

PON DER

The anamorphic lenses described in Section 448 are thick lenses Why can t a thin astigmatic lens be used as an anamorphic lens

The way to correct astigmatism is to use a lenamp that converges (or dishyverges) rays in one plane while not affecting rays in the perpendicular plane Such a lens is a cylindrical lens (Fig 65l which is curved in one direction but not in the pershypendicular direction as if cut out of a cylindemiddotr of glass (see the TRY IT) The ophthalmologist will then preshyscribe a certain amount of cylindrishycal curvature to your glasses specishyfying the orientation along which the cylinder is to lie Such astigmashytism may be concurrent with an overall myopia say In that case your prescription may have a sphershyical component of - 2 5 diopters and a cylindrical component of -075 diopters at a 100 orientation

FIGURE 65

Cylindrical lens Rays 7 and 2 in the horizontal plane are made to converge Rays 3 and 4 in the vertical plane are essentially unaffected

It has been suggested that El Greco had severe astigmatism which would make the world look elongated to him and that this is why he painted the elongated figshyures for which he is famous This is really no explanation His astigmashytism would have also made his paintings look elongated and his figures would have looked to him to be the same shape as his models only if they were in fact the same shape

TRY IT

FOR SECTON 628

A cylindrical lens

As described in the first TRY IT for Section 34A you can make a cylindrical lens by filling a straight-sided cylindrical jar with water Fill the jar about half full with water put the lid gn tightly and hold the jar on its side The top surface of the water is then the flat side of a plano-convex iens and the bottom (cuNed) surface is the convex side Hold the lens about t m above this page and look down through it at the print Keeping the lens still rotate the page Also try this with a pencil as the object instead of this page Try to ignore any wobbles due to nonuniformity of the glass You now have some idea of what an astigmatic eye sees

Hold the lens about 1 m above a piece of graph paper (or any crosshatched paper) with the length of the jar oriented parallel to one set of lines With your eyes close to the lens look down through the lens at the graph paper What happens to the lines running

parallel to the jar To the perpendicular set of lines Why

Use your lens to try to focus a line image of the sun (when it is overhead) or a high lightbulb onto a piece of paper Move the lens up or down until you have made the line as sharp as you can then measumiddotre its distance to the paper (the focal length of the cylindrical lens) in meters Determine the power of the lens in diopters If the jar had a larger diameter would the power be greater or smaller Find another jar and try it

C Contact lenses

Contact lenses correct viSion in essentially the same manner as glasses but they do have a few opshytical differences These lenses are worn in contact with the cornea hence the name The eye then sees the image at the same angle (detershymined by the central ray) as it would see the object without the lens so the image on the retina is the same size in either case In the case with eyeglasses the eye is at some distance from the lens so the image appears a different size than the object (Hold a lens from your glasses or a contact lens a few inches from your eye and look at an object that extends beyond the lens so you can compare object and image sizes)

PON DER

Why does the converging lens cause the image to look larger Try ray tracing using two lenses one to represent the converging lens and one to represent the lens of your eye

This magnification (for the hypershyopic eye) and shrinking (for the myshyopic eye) is generally inSignificant and rarely a reason to get contact lenses (When you first put on strong glasses the world may apshypear smaller or larger and seem to shift as you move your eyes Howshyever your brain soon compensates for this effect)

Whereas the orientation of the asshytigmatic correction in an eyeglass is important a spherical contact lens can correct for astigmatism even

62 SIlVGLEmiddotLENS IlVSTRUMENTS

without remaining In a single orishyentation The reason for this is that the contact lens the cornea and the tear fluid that fills the space beshytween them all have about the same index of refraction The only bendshying of light therefore occurs at the front surface of the contact lens (Fig 66) Since this surface is spherical there will be no astigmashytism (Soft contact lenses tend to be too flexible to correct astigmatism but hard contact lenses do It quite well)

Since your contact lens moves when your eye moves you cant look through different parts of the lens

FIGURE 66

(a) A contact lens on the cornea with tear fluid in between (b) Photograph of a contact lens

Fluid

Contac t lens

1--1-______ Cornea

(a)

163

for reading and for distant viewing as easily as you can with bifocal glasses However when you look down suffiCiently the motion of the contact lens is stopped by the lower lid so the contact lens slips on the cornea Bifocal contact lenses take advantage of this fact The outer part of the lens which is located over the pupil when you look down has a different curvature or index of refraction than the center of the lens (which is normally over the pushypil and which will return to that position when you look up in order to resume its tight fit to your corshynea)

D The magnifying glass

We have argued that if you place your eye immediately behind a conshyverging lens (which well see is a magnifying glass) the image apshypears the same size as the object did without the lens (see Fig 63d) One often sees movie detectives holding the magnifying glass at arms length In that case the image does appear larger than the object Nevertheless this is not the best way to hold the magnifying glass To get the largest image on your retina you should place your eye close to the magnifying glass at which distance the magnifying glass does not magnify The explashy

(b)

nation of this paradoxical stateshyment depends on the fact that the magnifying glass enables you to bring Objects very close to your eye and still keep them in focus The objects look big because being close they subtend a large angle Without the magnifying glass you would have to move the objects farshyther away in order to focus sharply on them and thus would have a smaller image on your retina

Lets see how this works In Figshyure 67a the object is located at the normal eyes near point 25 cm The image on the retina is shown its loshycation determined by the central ray alone (since we know the eye will focus It on the retina) In Figure 67b a larger retinal image Is obshytained with a magnifying glass (of focal length less than 25 cm) Here the object is located at the focal point of the lens and consequently the rays leaving the magnifying glass are parallel to each other as they enter the eye Such rays are foshycused by the relaxed eye Again the central ray locates the Image on the retina Because the object is closer the central ray makes a bigger angle with the axis in Figure 67b than in Figure 67a so the retinal image is larger The magnifying glass has done its job (The TRY IT suggests several ways to make a magnifying glass)

The magnification or magnifyshying p ower of a lens is usually given as the ratio of the image sizes in these two sltuttions (ie with and without the magnifying glass) which is equal to the ratio of the object distances

Magnifying power = 25ft (f in em)

For example iff = 100 mm = 10 cm the magnifying lens has magshynifying power of N = 25 This is written as 25X (and read as 25 power)

You can get somewhat greater magnification If you place the object closer than the focal point at the point where it forms a virtual image 25 cm from the eye (Fig 67c) Your eye can focus on this virtual image by accommodating which is more tiring than viewing with parallel

CHAPTER 6 OPTICAL INSTRUMENTS

164

Lens of

Objec t

Image

1~~~---------Retina

(a)

Magnifying

glass Lens of

Image

bullbull Object

~____ f __--I~

Retina

(b)

eye

- ----shy - shy - - -- shy

25 cm------------~

Magnifying Lens of Virtual glass eye image

- ------ ----- - - - -- shyImage

I ~1~~------------ 25 cm-------~ Retina

(e)

to make it as close to the virtual imshyFIG URE 67

age as possible) (a) Unaided normal eye object at near The same principle can be appliedpoint (b) Eye with magnifying glass to a camera for close-up photograshyimage at infinity (c) Eye with magnifying

phy A close-up lens is nothing butglass image at 25 cm Note the relative sizes of the images on the retinas The a magnifying glass Placed in front compound lens of the eye is treated as a of the camera lens it allows the thin lens in this figure camera to focus on very close obshy

jects Just as with the eye the camshyrays but does give a bigger retinal era actually focuses on the virtual image than that obtained in Figure image produced by the magnifying 67b The magnification is then glass For example if you place the larger (by 1) than the nominal magshy object at the focal point of the magshynifying power given by the formula nifying glass you should set the above (So our 25X magnifier acshy camera to focus at infinity tually magnifies 35 times used In principle by using a very short this way Of course you want the focal length lens you can make the eye as close to the lens as possible image on your retina (or film) as

large as you like Generally howshyever the aberrations become too large for magnifications much beshyyond 5X Weve seen tha t assuming enough light is available we can reshyduce aberrations by stopping down or using a smaller diameter lens This is just what van Leeuwenhoek (1632-1723) did with his pioneershying mic roscopes his lenses were pinhea d size ground with incredishyble skill and had focal lengths as short as I mm giving a magnifyshying power of 200 With good lightshying and careful mounting of such a tiny lens and the specimen he could see spermatozoa and other wee animals He opened up the world of microscopy with a microshyscope whose entire size was about two inches Modern microscopes are bigger and compound-they use more (han one lens It is interesting to note that the compound microshyscope was invented before Leeuwenshyhoek was born but his lenses were so far superior to the competition that he could do better with a simshyple magnifying glass

TRY IT

FOR SECTION 620

A water magnifying glass

If you have a spherical glass bottle you can make a thick lens by filling it with water (Secs 34A and 348) or make a plano-convex lens as in the TRY IT for Section 628 (One of the attractions of a wine glass besides its content is that the spherical lens formed by the wine in the round-bottom glass creates on the table cloth images of nearby candles The next time you re served wine while pretending to judge its color like a true connoisseur look through the wine at the inverted image of the room ) Spherical glass-bottle lenses were used to concentrate the light of a candle on fine work such as lace making (Fig 68) Such a lace-makers condenser was described by John White in 7657 under the heading How to make a glorious light with a candle like sunshine Round bottles of water left in an open window have been known to start fires when the

63 COMPOUND MICROSCOPES

165

fiGURE 68

Lacemakers condenser capable of focusing the light of a candle on the work of the lacemaker

sun moved into the right position In Jules Vernes Mysterious Island the heroes who are stranded on a desert island without matches (of course) make a lens by holding water between the glasses from two pocket watches The lens is then used as a burning glass to start a fire

A water droplet that makes a nice lens can be formed with an eyedropper If you hold the drop in front of a printed page you should be able to measure its focal length-roughly the greatest distance from the page that you can hold the drop and still see an erect image (You may have to examine the image with another magnifying glass) Your drop will probably be bigger than Leeuwenhoeks lenses so youll get some idea of the viewing problems he had (You can also measure the focal length by the method of the TRY IT for Sec 348)

To hold a slightly larger droplet pierce a piece of aluminum foil with the tip of a pencil and rotate the pencil making a reasonab ly round hole about 5 mm in diameter Pour a little water over the hole in the foil to form a droplet of water across it that can be used as a magnifying glass (Alternatively a wire loop of the same diameter can be used) Looking through the droplet you can estimate its

focal length and magnification power Th e focal length should be quite small (about 75 cm which means a 76X magnifier)

A way to make a larger water lens is to freeze the water in the bottom of a spherically shaped bowl The water will freeze from the outside inward and concentrate the less easily frozen impurities on the inside as well as developing bumps and cracks as it freezes leaving you with a rather foggy lens that scatters the light instead of focusing it If you freeze the water slowly and take it out of the freezer before the last bit of water is frozen you can get a reasonably clear lens In the short time before your ice lens drips all over everything you should be able to verify that it is a magnifying glass and make some estimates of its magnifying power and focal length It is very hard to get any kind of decent image from an ice lens but you may be able to concentrate the suns rays enough to use the lens as a burning glass as Richard Adams describes in The Girl in a Swing

You dont know about the ice-bum Ill tell you Sometimes in the North in winter the iceJorms rtght across the curved top oj a hill Then when the sun shines the ice becomes like a magnifying glass so that the sun bums off all the grass and heather undemeath Later the ice melts and all through sprtng the hills bare until the grass grows again Dont you see the ice is what burns-the last thing youd expect to burn anything and yet it does

6 3 COMPOUND MICROSCOPES

The compound microscope uses a magnifying glass not to look dishyrectly at the object but rather to look at a real image created by anshyother lens Consider the Simplified compound microscope shown in Figure 69a (The TRY IT at the end of Sec 64B tells you how to make one) The first lens called the obshyjective because it is closest to the object PQ forms a real image PQ the intermediate image The viewer looks at this real image with a magshynifying glass called the eyepiece or ocular For viewing with relaxed eye muscles the rays leaving the eyepiece should be parallel to one another This means that the ~yeshypiece should be located at its focal distancefe from the intermediate image (see the figure and the imshyportant note in its caption) In orshyder to eliminate any stray light the two lenses are encased in the ends of a tube Sometimes a calibrated length scale called a graticule is drawn on a thin glass disk located in the plane of the intermediate imshyage This allows measurement of the size of objects observed in the microscope

Both lenses then provide magshynification As with any magnifying glass the shorter the focallengthfe the greater the magnification of the eyepiece The magnification of the objective is determined by the intershymediate image size PQ compared to the Object size PQ The location of the intermediate image is fixed because it must be at the focal point of the eyepiece and the spacshying between the lenses is usually fixed at about 18 cm so the viewers eye can be at a convenient height above the work table You can see by examining the central ray 2 that a larger image at that lecation means the object must be closer to the objective This can be accomshyplished with a smaller objective foshycallengthJo (Fig 69b) That is for larger magnification we want both

10 andfe smaller For the same diameter a smaller

CHAPTER 6 OPTICAL INSTRUMENTS

160

I ~ I Distance to far point(a)

0 0

I Distance to far point = Focal length (b)

is at some closer distance say at 50 cm (Fig 6 2a) (This close distance would correspond to the power of the eyes compound lens being only 3 too large) If the eyes accomshymodation is normal (4 diopters) its near point is then closer than the normal near point (in this case it turns out to be 17 cm) Thus a myshyopic person has only a relatively small range of distances over which she can see clearly but at the near point she can see a larger more deshytailed image of the object than a normal viewer can at his near point-the myope has a kind of built-In magnifying glass In fact if your eye is normal and you want to know how the world looks to a myshyope you need only look through a magnifying glass held close to your eye Since magnifying glasses were not used as visual aids until the thirteenth century it has been sugshygested that the artisans responsible for the delicate engraving found in jewelry and coins from well before that time were actually myopic Being hereditary this trait as well as the tricks of the engraving trade would have been handed down from one generation of artisans to the next

The cure for a myopic eye is a dishyverging eyeglass whose negative power decreases the eyes excessive power and moves the far point back

FIGURE 62

Relaxed myopic eye (a) without glasses (b) with glasses The diverging lens is drawn separated from the eye to show that the rays leaving the glasses look as in (a) but there need be no separation the correction works also for contact lenses

to infinity where it belongs Altershynatively put it bends parallel rays from distant objects so that they appear to be coming from a virtual image If this image is located at the far point the relaxed myopic eye can see it clearly (see Fig 62b and compare with Fig 323a) Hence the lens must have a focal length equal to the distance to the far point of the relaxed myopic eye For our example where the far point is at 50 cm the proper diverging eyeshyglass has] = -50 cm = - 1 m so the prescription for this lens would read - 2 diopters (The normal eyes compound lens has a power of about 60 diopters when relaxed The myopic eye in this case had the excessive power of 62 diopters the eyeglasses reduce it back to the normal value)

Now consider the hyperopic eye Its power is too small in the relaxed state-suppose it is only 57 diOpshyters This hyperope already has to accommodate (by 3 diopters) to the normal value of 60 diopters in order

to see distant objects (Fig 63a) However the very highest power he can reach by accommodation is 61 diopters Since this is only 1 diopshyter above that necessary to see disshytant objects his near point is at 1 m (see Figs 63b and c) To see objects that close he must use all his accommodation ability thereshyfore he cannot focus on anything closer

The cure for this eye is a convergshying eyeglass that raises the power by 3 diopters to reach the normal 64 diopters when fully accommoshydated That is the prescription would read + 3 diopters Consider the effect of such an eyeglass lens on an object at the normal near point of 25 cm It will make a virshytual image at 1 m where the hypershyopic eye can see it (See Fig 63d and try the construction by ray tracing)

As the accommodated uncorshyrected hyperopic eye can focus on distant objects hyperopic people were once called farsighted Simishylarly the extra strong myopic eye when fully accommodated can foshycus on objects closer than the norshymal 25 cm and was therefore called nearsighted These names howshyever are misleading if the eye cant accommodate properly as often happens as you grow older The agshying process adds flatter layers to the eyelens (see Fig 59) These layers not only reduce the eyelens power (reducing any myopia that may be present) but also separate the inshyner core from the humors that bathe the eyelens This older inner core then tends to become less flexshyible and pliant and the eye does not accommodate as well This condishytion called presbyopia prevents an otherwise normal eye from foshycusing on near Objects In his poem Typical Optical John Upshydike writes

In the days oj my youth mid many a caper

[ drew with my nose a mere inchJrom the paper

but now that Im older and life h as grown hard

[find [ cantJocus inside oj a yard

Greek presbus old man

-

62 SINGLE-LENS INSTRUMENTS

161

(a)

0 bullbull 0shy

0

1---- 25 em - ----gt11 (b)

_------ Distanee to near point-------~

(e)

+Q

~ ~middotf ~1~SJ

-_---r---- D lt0 ~~ ~ (d)

FIGURE 63

The hyperopic eye (a) partially accommodated (b) fully accommodated object at 25 cm (c) fully accommodated object at near point (d) corrected fully accommodated object at 25 em appears to be at near pOint

The aged eye may then require one eyeglass prescription for distant viewing and another for close-up The two lenses are often combined

into a bifocal lens with the closeshyup lens in the lower half of the frame (since you generally look downward toward close objects) Bishyfocals can now be made in which the lenses in the two halves gradushyally fade into one another thus eliminating the conspicuous line across the lens

Convex lenses for the hyperopic eye were in use at the end of the thirteenth century but it was a

century and a half later before conshycave lenses appeared for the more common myopic eye It was another century or so before anybody undershystood how these lenses worked to assist the eye

B Eyeglasses cylindrical correction

Another common eye defect astigshymatism occurs when the cornea is not spherical but is more curved in one plane than in another That is the focal length of the astigmatic eye is different for rays in one plane than for those in a perpendicular plane It cannot for example focus simultaneously on both the horishyzontal and vertical glazing bars of a window Figure 64 provides a sim-

FIGURE 64

Test for astigmatism Close one eye and view this figure through the other eye (without glasses or contact lenses) Hold the figure sufficiently close to the eye so that all lines look blurred Then gradually move the figure away until one set of lines comes into focus with the rest blurred (If two adjacent sets come into focus together rotate the figure a little until only one is in focus If all sets come into focus together you don t have astigmatism ) You have now found the near pOint for a line in the direction of the lines that are in focus Move the pattern away further until the lines perpendicular to the first set come into focus (The first set mayor may not remain in focus) This is the near po int for a line perpendicular to the o riginal set The different near points mean that your eye has a different focal length for lines parallel to and perpendicular to the original set Try the procedure again with your glasses or contact lenses to see if your astigmatism is corrected

CHAPTER 6 OPTICAL INSTRUMENTS

162

pie test for astigmatism in your eyes (The difference in focal length in the defect astigmatism occurs all over the field of view it should not be confused with the off-axis abershyration astigmatism Sec 3 5D )

PON DER

The anamorphic lenses described in Section 448 are thick lenses Why can t a thin astigmatic lens be used as an anamorphic lens

The way to correct astigmatism is to use a lenamp that converges (or dishyverges) rays in one plane while not affecting rays in the perpendicular plane Such a lens is a cylindrical lens (Fig 65l which is curved in one direction but not in the pershypendicular direction as if cut out of a cylindemiddotr of glass (see the TRY IT) The ophthalmologist will then preshyscribe a certain amount of cylindrishycal curvature to your glasses specishyfying the orientation along which the cylinder is to lie Such astigmashytism may be concurrent with an overall myopia say In that case your prescription may have a sphershyical component of - 2 5 diopters and a cylindrical component of -075 diopters at a 100 orientation

FIGURE 65

Cylindrical lens Rays 7 and 2 in the horizontal plane are made to converge Rays 3 and 4 in the vertical plane are essentially unaffected

It has been suggested that El Greco had severe astigmatism which would make the world look elongated to him and that this is why he painted the elongated figshyures for which he is famous This is really no explanation His astigmashytism would have also made his paintings look elongated and his figures would have looked to him to be the same shape as his models only if they were in fact the same shape

TRY IT

FOR SECTON 628

A cylindrical lens

As described in the first TRY IT for Section 34A you can make a cylindrical lens by filling a straight-sided cylindrical jar with water Fill the jar about half full with water put the lid gn tightly and hold the jar on its side The top surface of the water is then the flat side of a plano-convex iens and the bottom (cuNed) surface is the convex side Hold the lens about t m above this page and look down through it at the print Keeping the lens still rotate the page Also try this with a pencil as the object instead of this page Try to ignore any wobbles due to nonuniformity of the glass You now have some idea of what an astigmatic eye sees

Hold the lens about 1 m above a piece of graph paper (or any crosshatched paper) with the length of the jar oriented parallel to one set of lines With your eyes close to the lens look down through the lens at the graph paper What happens to the lines running

parallel to the jar To the perpendicular set of lines Why

Use your lens to try to focus a line image of the sun (when it is overhead) or a high lightbulb onto a piece of paper Move the lens up or down until you have made the line as sharp as you can then measumiddotre its distance to the paper (the focal length of the cylindrical lens) in meters Determine the power of the lens in diopters If the jar had a larger diameter would the power be greater or smaller Find another jar and try it

C Contact lenses

Contact lenses correct viSion in essentially the same manner as glasses but they do have a few opshytical differences These lenses are worn in contact with the cornea hence the name The eye then sees the image at the same angle (detershymined by the central ray) as it would see the object without the lens so the image on the retina is the same size in either case In the case with eyeglasses the eye is at some distance from the lens so the image appears a different size than the object (Hold a lens from your glasses or a contact lens a few inches from your eye and look at an object that extends beyond the lens so you can compare object and image sizes)

PON DER

Why does the converging lens cause the image to look larger Try ray tracing using two lenses one to represent the converging lens and one to represent the lens of your eye

This magnification (for the hypershyopic eye) and shrinking (for the myshyopic eye) is generally inSignificant and rarely a reason to get contact lenses (When you first put on strong glasses the world may apshypear smaller or larger and seem to shift as you move your eyes Howshyever your brain soon compensates for this effect)

Whereas the orientation of the asshytigmatic correction in an eyeglass is important a spherical contact lens can correct for astigmatism even

62 SIlVGLEmiddotLENS IlVSTRUMENTS

without remaining In a single orishyentation The reason for this is that the contact lens the cornea and the tear fluid that fills the space beshytween them all have about the same index of refraction The only bendshying of light therefore occurs at the front surface of the contact lens (Fig 66) Since this surface is spherical there will be no astigmashytism (Soft contact lenses tend to be too flexible to correct astigmatism but hard contact lenses do It quite well)

Since your contact lens moves when your eye moves you cant look through different parts of the lens

FIGURE 66

(a) A contact lens on the cornea with tear fluid in between (b) Photograph of a contact lens

Fluid

Contac t lens

1--1-______ Cornea

(a)

163

for reading and for distant viewing as easily as you can with bifocal glasses However when you look down suffiCiently the motion of the contact lens is stopped by the lower lid so the contact lens slips on the cornea Bifocal contact lenses take advantage of this fact The outer part of the lens which is located over the pupil when you look down has a different curvature or index of refraction than the center of the lens (which is normally over the pushypil and which will return to that position when you look up in order to resume its tight fit to your corshynea)

D The magnifying glass

We have argued that if you place your eye immediately behind a conshyverging lens (which well see is a magnifying glass) the image apshypears the same size as the object did without the lens (see Fig 63d) One often sees movie detectives holding the magnifying glass at arms length In that case the image does appear larger than the object Nevertheless this is not the best way to hold the magnifying glass To get the largest image on your retina you should place your eye close to the magnifying glass at which distance the magnifying glass does not magnify The explashy

(b)

nation of this paradoxical stateshyment depends on the fact that the magnifying glass enables you to bring Objects very close to your eye and still keep them in focus The objects look big because being close they subtend a large angle Without the magnifying glass you would have to move the objects farshyther away in order to focus sharply on them and thus would have a smaller image on your retina

Lets see how this works In Figshyure 67a the object is located at the normal eyes near point 25 cm The image on the retina is shown its loshycation determined by the central ray alone (since we know the eye will focus It on the retina) In Figure 67b a larger retinal image Is obshytained with a magnifying glass (of focal length less than 25 cm) Here the object is located at the focal point of the lens and consequently the rays leaving the magnifying glass are parallel to each other as they enter the eye Such rays are foshycused by the relaxed eye Again the central ray locates the Image on the retina Because the object is closer the central ray makes a bigger angle with the axis in Figure 67b than in Figure 67a so the retinal image is larger The magnifying glass has done its job (The TRY IT suggests several ways to make a magnifying glass)

The magnification or magnifyshying p ower of a lens is usually given as the ratio of the image sizes in these two sltuttions (ie with and without the magnifying glass) which is equal to the ratio of the object distances

Magnifying power = 25ft (f in em)

For example iff = 100 mm = 10 cm the magnifying lens has magshynifying power of N = 25 This is written as 25X (and read as 25 power)

You can get somewhat greater magnification If you place the object closer than the focal point at the point where it forms a virtual image 25 cm from the eye (Fig 67c) Your eye can focus on this virtual image by accommodating which is more tiring than viewing with parallel

CHAPTER 6 OPTICAL INSTRUMENTS

164

Lens of

Objec t

Image

1~~~---------Retina

(a)

Magnifying

glass Lens of

Image

bullbull Object

~____ f __--I~

Retina

(b)

eye

- ----shy - shy - - -- shy

25 cm------------~

Magnifying Lens of Virtual glass eye image

- ------ ----- - - - -- shyImage

I ~1~~------------ 25 cm-------~ Retina

(e)

to make it as close to the virtual imshyFIG URE 67

age as possible) (a) Unaided normal eye object at near The same principle can be appliedpoint (b) Eye with magnifying glass to a camera for close-up photograshyimage at infinity (c) Eye with magnifying

phy A close-up lens is nothing butglass image at 25 cm Note the relative sizes of the images on the retinas The a magnifying glass Placed in front compound lens of the eye is treated as a of the camera lens it allows the thin lens in this figure camera to focus on very close obshy

jects Just as with the eye the camshyrays but does give a bigger retinal era actually focuses on the virtual image than that obtained in Figure image produced by the magnifying 67b The magnification is then glass For example if you place the larger (by 1) than the nominal magshy object at the focal point of the magshynifying power given by the formula nifying glass you should set the above (So our 25X magnifier acshy camera to focus at infinity tually magnifies 35 times used In principle by using a very short this way Of course you want the focal length lens you can make the eye as close to the lens as possible image on your retina (or film) as

large as you like Generally howshyever the aberrations become too large for magnifications much beshyyond 5X Weve seen tha t assuming enough light is available we can reshyduce aberrations by stopping down or using a smaller diameter lens This is just what van Leeuwenhoek (1632-1723) did with his pioneershying mic roscopes his lenses were pinhea d size ground with incredishyble skill and had focal lengths as short as I mm giving a magnifyshying power of 200 With good lightshying and careful mounting of such a tiny lens and the specimen he could see spermatozoa and other wee animals He opened up the world of microscopy with a microshyscope whose entire size was about two inches Modern microscopes are bigger and compound-they use more (han one lens It is interesting to note that the compound microshyscope was invented before Leeuwenshyhoek was born but his lenses were so far superior to the competition that he could do better with a simshyple magnifying glass

TRY IT

FOR SECTION 620

A water magnifying glass

If you have a spherical glass bottle you can make a thick lens by filling it with water (Secs 34A and 348) or make a plano-convex lens as in the TRY IT for Section 628 (One of the attractions of a wine glass besides its content is that the spherical lens formed by the wine in the round-bottom glass creates on the table cloth images of nearby candles The next time you re served wine while pretending to judge its color like a true connoisseur look through the wine at the inverted image of the room ) Spherical glass-bottle lenses were used to concentrate the light of a candle on fine work such as lace making (Fig 68) Such a lace-makers condenser was described by John White in 7657 under the heading How to make a glorious light with a candle like sunshine Round bottles of water left in an open window have been known to start fires when the

63 COMPOUND MICROSCOPES

165

fiGURE 68

Lacemakers condenser capable of focusing the light of a candle on the work of the lacemaker

sun moved into the right position In Jules Vernes Mysterious Island the heroes who are stranded on a desert island without matches (of course) make a lens by holding water between the glasses from two pocket watches The lens is then used as a burning glass to start a fire

A water droplet that makes a nice lens can be formed with an eyedropper If you hold the drop in front of a printed page you should be able to measure its focal length-roughly the greatest distance from the page that you can hold the drop and still see an erect image (You may have to examine the image with another magnifying glass) Your drop will probably be bigger than Leeuwenhoeks lenses so youll get some idea of the viewing problems he had (You can also measure the focal length by the method of the TRY IT for Sec 348)

To hold a slightly larger droplet pierce a piece of aluminum foil with the tip of a pencil and rotate the pencil making a reasonab ly round hole about 5 mm in diameter Pour a little water over the hole in the foil to form a droplet of water across it that can be used as a magnifying glass (Alternatively a wire loop of the same diameter can be used) Looking through the droplet you can estimate its

focal length and magnification power Th e focal length should be quite small (about 75 cm which means a 76X magnifier)

A way to make a larger water lens is to freeze the water in the bottom of a spherically shaped bowl The water will freeze from the outside inward and concentrate the less easily frozen impurities on the inside as well as developing bumps and cracks as it freezes leaving you with a rather foggy lens that scatters the light instead of focusing it If you freeze the water slowly and take it out of the freezer before the last bit of water is frozen you can get a reasonably clear lens In the short time before your ice lens drips all over everything you should be able to verify that it is a magnifying glass and make some estimates of its magnifying power and focal length It is very hard to get any kind of decent image from an ice lens but you may be able to concentrate the suns rays enough to use the lens as a burning glass as Richard Adams describes in The Girl in a Swing

You dont know about the ice-bum Ill tell you Sometimes in the North in winter the iceJorms rtght across the curved top oj a hill Then when the sun shines the ice becomes like a magnifying glass so that the sun bums off all the grass and heather undemeath Later the ice melts and all through sprtng the hills bare until the grass grows again Dont you see the ice is what burns-the last thing youd expect to burn anything and yet it does

6 3 COMPOUND MICROSCOPES

The compound microscope uses a magnifying glass not to look dishyrectly at the object but rather to look at a real image created by anshyother lens Consider the Simplified compound microscope shown in Figure 69a (The TRY IT at the end of Sec 64B tells you how to make one) The first lens called the obshyjective because it is closest to the object PQ forms a real image PQ the intermediate image The viewer looks at this real image with a magshynifying glass called the eyepiece or ocular For viewing with relaxed eye muscles the rays leaving the eyepiece should be parallel to one another This means that the ~yeshypiece should be located at its focal distancefe from the intermediate image (see the figure and the imshyportant note in its caption) In orshyder to eliminate any stray light the two lenses are encased in the ends of a tube Sometimes a calibrated length scale called a graticule is drawn on a thin glass disk located in the plane of the intermediate imshyage This allows measurement of the size of objects observed in the microscope

Both lenses then provide magshynification As with any magnifying glass the shorter the focallengthfe the greater the magnification of the eyepiece The magnification of the objective is determined by the intershymediate image size PQ compared to the Object size PQ The location of the intermediate image is fixed because it must be at the focal point of the eyepiece and the spacshying between the lenses is usually fixed at about 18 cm so the viewers eye can be at a convenient height above the work table You can see by examining the central ray 2 that a larger image at that lecation means the object must be closer to the objective This can be accomshyplished with a smaller objective foshycallengthJo (Fig 69b) That is for larger magnification we want both

10 andfe smaller For the same diameter a smaller

62 SINGLE-LENS INSTRUMENTS

161

(a)

0 bullbull 0shy

0

1---- 25 em - ----gt11 (b)

_------ Distanee to near point-------~

(e)

+Q

~ ~middotf ~1~SJ

-_---r---- D lt0 ~~ ~ (d)

FIGURE 63

The hyperopic eye (a) partially accommodated (b) fully accommodated object at 25 cm (c) fully accommodated object at near point (d) corrected fully accommodated object at 25 em appears to be at near pOint

The aged eye may then require one eyeglass prescription for distant viewing and another for close-up The two lenses are often combined

into a bifocal lens with the closeshyup lens in the lower half of the frame (since you generally look downward toward close objects) Bishyfocals can now be made in which the lenses in the two halves gradushyally fade into one another thus eliminating the conspicuous line across the lens

Convex lenses for the hyperopic eye were in use at the end of the thirteenth century but it was a

century and a half later before conshycave lenses appeared for the more common myopic eye It was another century or so before anybody undershystood how these lenses worked to assist the eye

B Eyeglasses cylindrical correction

Another common eye defect astigshymatism occurs when the cornea is not spherical but is more curved in one plane than in another That is the focal length of the astigmatic eye is different for rays in one plane than for those in a perpendicular plane It cannot for example focus simultaneously on both the horishyzontal and vertical glazing bars of a window Figure 64 provides a sim-

FIGURE 64

Test for astigmatism Close one eye and view this figure through the other eye (without glasses or contact lenses) Hold the figure sufficiently close to the eye so that all lines look blurred Then gradually move the figure away until one set of lines comes into focus with the rest blurred (If two adjacent sets come into focus together rotate the figure a little until only one is in focus If all sets come into focus together you don t have astigmatism ) You have now found the near pOint for a line in the direction of the lines that are in focus Move the pattern away further until the lines perpendicular to the first set come into focus (The first set mayor may not remain in focus) This is the near po int for a line perpendicular to the o riginal set The different near points mean that your eye has a different focal length for lines parallel to and perpendicular to the original set Try the procedure again with your glasses or contact lenses to see if your astigmatism is corrected

CHAPTER 6 OPTICAL INSTRUMENTS

162

pie test for astigmatism in your eyes (The difference in focal length in the defect astigmatism occurs all over the field of view it should not be confused with the off-axis abershyration astigmatism Sec 3 5D )

PON DER

The anamorphic lenses described in Section 448 are thick lenses Why can t a thin astigmatic lens be used as an anamorphic lens

The way to correct astigmatism is to use a lenamp that converges (or dishyverges) rays in one plane while not affecting rays in the perpendicular plane Such a lens is a cylindrical lens (Fig 65l which is curved in one direction but not in the pershypendicular direction as if cut out of a cylindemiddotr of glass (see the TRY IT) The ophthalmologist will then preshyscribe a certain amount of cylindrishycal curvature to your glasses specishyfying the orientation along which the cylinder is to lie Such astigmashytism may be concurrent with an overall myopia say In that case your prescription may have a sphershyical component of - 2 5 diopters and a cylindrical component of -075 diopters at a 100 orientation

FIGURE 65

Cylindrical lens Rays 7 and 2 in the horizontal plane are made to converge Rays 3 and 4 in the vertical plane are essentially unaffected

It has been suggested that El Greco had severe astigmatism which would make the world look elongated to him and that this is why he painted the elongated figshyures for which he is famous This is really no explanation His astigmashytism would have also made his paintings look elongated and his figures would have looked to him to be the same shape as his models only if they were in fact the same shape

TRY IT

FOR SECTON 628

A cylindrical lens

As described in the first TRY IT for Section 34A you can make a cylindrical lens by filling a straight-sided cylindrical jar with water Fill the jar about half full with water put the lid gn tightly and hold the jar on its side The top surface of the water is then the flat side of a plano-convex iens and the bottom (cuNed) surface is the convex side Hold the lens about t m above this page and look down through it at the print Keeping the lens still rotate the page Also try this with a pencil as the object instead of this page Try to ignore any wobbles due to nonuniformity of the glass You now have some idea of what an astigmatic eye sees

Hold the lens about 1 m above a piece of graph paper (or any crosshatched paper) with the length of the jar oriented parallel to one set of lines With your eyes close to the lens look down through the lens at the graph paper What happens to the lines running

parallel to the jar To the perpendicular set of lines Why

Use your lens to try to focus a line image of the sun (when it is overhead) or a high lightbulb onto a piece of paper Move the lens up or down until you have made the line as sharp as you can then measumiddotre its distance to the paper (the focal length of the cylindrical lens) in meters Determine the power of the lens in diopters If the jar had a larger diameter would the power be greater or smaller Find another jar and try it

C Contact lenses

Contact lenses correct viSion in essentially the same manner as glasses but they do have a few opshytical differences These lenses are worn in contact with the cornea hence the name The eye then sees the image at the same angle (detershymined by the central ray) as it would see the object without the lens so the image on the retina is the same size in either case In the case with eyeglasses the eye is at some distance from the lens so the image appears a different size than the object (Hold a lens from your glasses or a contact lens a few inches from your eye and look at an object that extends beyond the lens so you can compare object and image sizes)

PON DER

Why does the converging lens cause the image to look larger Try ray tracing using two lenses one to represent the converging lens and one to represent the lens of your eye

This magnification (for the hypershyopic eye) and shrinking (for the myshyopic eye) is generally inSignificant and rarely a reason to get contact lenses (When you first put on strong glasses the world may apshypear smaller or larger and seem to shift as you move your eyes Howshyever your brain soon compensates for this effect)

Whereas the orientation of the asshytigmatic correction in an eyeglass is important a spherical contact lens can correct for astigmatism even

62 SIlVGLEmiddotLENS IlVSTRUMENTS

without remaining In a single orishyentation The reason for this is that the contact lens the cornea and the tear fluid that fills the space beshytween them all have about the same index of refraction The only bendshying of light therefore occurs at the front surface of the contact lens (Fig 66) Since this surface is spherical there will be no astigmashytism (Soft contact lenses tend to be too flexible to correct astigmatism but hard contact lenses do It quite well)

Since your contact lens moves when your eye moves you cant look through different parts of the lens

FIGURE 66

(a) A contact lens on the cornea with tear fluid in between (b) Photograph of a contact lens

Fluid

Contac t lens

1--1-______ Cornea

(a)

163

for reading and for distant viewing as easily as you can with bifocal glasses However when you look down suffiCiently the motion of the contact lens is stopped by the lower lid so the contact lens slips on the cornea Bifocal contact lenses take advantage of this fact The outer part of the lens which is located over the pupil when you look down has a different curvature or index of refraction than the center of the lens (which is normally over the pushypil and which will return to that position when you look up in order to resume its tight fit to your corshynea)

D The magnifying glass

We have argued that if you place your eye immediately behind a conshyverging lens (which well see is a magnifying glass) the image apshypears the same size as the object did without the lens (see Fig 63d) One often sees movie detectives holding the magnifying glass at arms length In that case the image does appear larger than the object Nevertheless this is not the best way to hold the magnifying glass To get the largest image on your retina you should place your eye close to the magnifying glass at which distance the magnifying glass does not magnify The explashy

(b)

nation of this paradoxical stateshyment depends on the fact that the magnifying glass enables you to bring Objects very close to your eye and still keep them in focus The objects look big because being close they subtend a large angle Without the magnifying glass you would have to move the objects farshyther away in order to focus sharply on them and thus would have a smaller image on your retina

Lets see how this works In Figshyure 67a the object is located at the normal eyes near point 25 cm The image on the retina is shown its loshycation determined by the central ray alone (since we know the eye will focus It on the retina) In Figure 67b a larger retinal image Is obshytained with a magnifying glass (of focal length less than 25 cm) Here the object is located at the focal point of the lens and consequently the rays leaving the magnifying glass are parallel to each other as they enter the eye Such rays are foshycused by the relaxed eye Again the central ray locates the Image on the retina Because the object is closer the central ray makes a bigger angle with the axis in Figure 67b than in Figure 67a so the retinal image is larger The magnifying glass has done its job (The TRY IT suggests several ways to make a magnifying glass)

The magnification or magnifyshying p ower of a lens is usually given as the ratio of the image sizes in these two sltuttions (ie with and without the magnifying glass) which is equal to the ratio of the object distances

Magnifying power = 25ft (f in em)

For example iff = 100 mm = 10 cm the magnifying lens has magshynifying power of N = 25 This is written as 25X (and read as 25 power)

You can get somewhat greater magnification If you place the object closer than the focal point at the point where it forms a virtual image 25 cm from the eye (Fig 67c) Your eye can focus on this virtual image by accommodating which is more tiring than viewing with parallel

CHAPTER 6 OPTICAL INSTRUMENTS

164

Lens of

Objec t

Image

1~~~---------Retina

(a)

Magnifying

glass Lens of

Image

bullbull Object

~____ f __--I~

Retina

(b)

eye

- ----shy - shy - - -- shy

25 cm------------~

Magnifying Lens of Virtual glass eye image

- ------ ----- - - - -- shyImage

I ~1~~------------ 25 cm-------~ Retina

(e)

to make it as close to the virtual imshyFIG URE 67

age as possible) (a) Unaided normal eye object at near The same principle can be appliedpoint (b) Eye with magnifying glass to a camera for close-up photograshyimage at infinity (c) Eye with magnifying

phy A close-up lens is nothing butglass image at 25 cm Note the relative sizes of the images on the retinas The a magnifying glass Placed in front compound lens of the eye is treated as a of the camera lens it allows the thin lens in this figure camera to focus on very close obshy

jects Just as with the eye the camshyrays but does give a bigger retinal era actually focuses on the virtual image than that obtained in Figure image produced by the magnifying 67b The magnification is then glass For example if you place the larger (by 1) than the nominal magshy object at the focal point of the magshynifying power given by the formula nifying glass you should set the above (So our 25X magnifier acshy camera to focus at infinity tually magnifies 35 times used In principle by using a very short this way Of course you want the focal length lens you can make the eye as close to the lens as possible image on your retina (or film) as

large as you like Generally howshyever the aberrations become too large for magnifications much beshyyond 5X Weve seen tha t assuming enough light is available we can reshyduce aberrations by stopping down or using a smaller diameter lens This is just what van Leeuwenhoek (1632-1723) did with his pioneershying mic roscopes his lenses were pinhea d size ground with incredishyble skill and had focal lengths as short as I mm giving a magnifyshying power of 200 With good lightshying and careful mounting of such a tiny lens and the specimen he could see spermatozoa and other wee animals He opened up the world of microscopy with a microshyscope whose entire size was about two inches Modern microscopes are bigger and compound-they use more (han one lens It is interesting to note that the compound microshyscope was invented before Leeuwenshyhoek was born but his lenses were so far superior to the competition that he could do better with a simshyple magnifying glass

TRY IT

FOR SECTION 620

A water magnifying glass

If you have a spherical glass bottle you can make a thick lens by filling it with water (Secs 34A and 348) or make a plano-convex lens as in the TRY IT for Section 628 (One of the attractions of a wine glass besides its content is that the spherical lens formed by the wine in the round-bottom glass creates on the table cloth images of nearby candles The next time you re served wine while pretending to judge its color like a true connoisseur look through the wine at the inverted image of the room ) Spherical glass-bottle lenses were used to concentrate the light of a candle on fine work such as lace making (Fig 68) Such a lace-makers condenser was described by John White in 7657 under the heading How to make a glorious light with a candle like sunshine Round bottles of water left in an open window have been known to start fires when the

63 COMPOUND MICROSCOPES

165

fiGURE 68

Lacemakers condenser capable of focusing the light of a candle on the work of the lacemaker

sun moved into the right position In Jules Vernes Mysterious Island the heroes who are stranded on a desert island without matches (of course) make a lens by holding water between the glasses from two pocket watches The lens is then used as a burning glass to start a fire

A water droplet that makes a nice lens can be formed with an eyedropper If you hold the drop in front of a printed page you should be able to measure its focal length-roughly the greatest distance from the page that you can hold the drop and still see an erect image (You may have to examine the image with another magnifying glass) Your drop will probably be bigger than Leeuwenhoeks lenses so youll get some idea of the viewing problems he had (You can also measure the focal length by the method of the TRY IT for Sec 348)

To hold a slightly larger droplet pierce a piece of aluminum foil with the tip of a pencil and rotate the pencil making a reasonab ly round hole about 5 mm in diameter Pour a little water over the hole in the foil to form a droplet of water across it that can be used as a magnifying glass (Alternatively a wire loop of the same diameter can be used) Looking through the droplet you can estimate its

focal length and magnification power Th e focal length should be quite small (about 75 cm which means a 76X magnifier)

A way to make a larger water lens is to freeze the water in the bottom of a spherically shaped bowl The water will freeze from the outside inward and concentrate the less easily frozen impurities on the inside as well as developing bumps and cracks as it freezes leaving you with a rather foggy lens that scatters the light instead of focusing it If you freeze the water slowly and take it out of the freezer before the last bit of water is frozen you can get a reasonably clear lens In the short time before your ice lens drips all over everything you should be able to verify that it is a magnifying glass and make some estimates of its magnifying power and focal length It is very hard to get any kind of decent image from an ice lens but you may be able to concentrate the suns rays enough to use the lens as a burning glass as Richard Adams describes in The Girl in a Swing

You dont know about the ice-bum Ill tell you Sometimes in the North in winter the iceJorms rtght across the curved top oj a hill Then when the sun shines the ice becomes like a magnifying glass so that the sun bums off all the grass and heather undemeath Later the ice melts and all through sprtng the hills bare until the grass grows again Dont you see the ice is what burns-the last thing youd expect to burn anything and yet it does

6 3 COMPOUND MICROSCOPES

The compound microscope uses a magnifying glass not to look dishyrectly at the object but rather to look at a real image created by anshyother lens Consider the Simplified compound microscope shown in Figure 69a (The TRY IT at the end of Sec 64B tells you how to make one) The first lens called the obshyjective because it is closest to the object PQ forms a real image PQ the intermediate image The viewer looks at this real image with a magshynifying glass called the eyepiece or ocular For viewing with relaxed eye muscles the rays leaving the eyepiece should be parallel to one another This means that the ~yeshypiece should be located at its focal distancefe from the intermediate image (see the figure and the imshyportant note in its caption) In orshyder to eliminate any stray light the two lenses are encased in the ends of a tube Sometimes a calibrated length scale called a graticule is drawn on a thin glass disk located in the plane of the intermediate imshyage This allows measurement of the size of objects observed in the microscope

Both lenses then provide magshynification As with any magnifying glass the shorter the focallengthfe the greater the magnification of the eyepiece The magnification of the objective is determined by the intershymediate image size PQ compared to the Object size PQ The location of the intermediate image is fixed because it must be at the focal point of the eyepiece and the spacshying between the lenses is usually fixed at about 18 cm so the viewers eye can be at a convenient height above the work table You can see by examining the central ray 2 that a larger image at that lecation means the object must be closer to the objective This can be accomshyplished with a smaller objective foshycallengthJo (Fig 69b) That is for larger magnification we want both

10 andfe smaller For the same diameter a smaller

CHAPTER 6 OPTICAL INSTRUMENTS

162

pie test for astigmatism in your eyes (The difference in focal length in the defect astigmatism occurs all over the field of view it should not be confused with the off-axis abershyration astigmatism Sec 3 5D )

PON DER

The anamorphic lenses described in Section 448 are thick lenses Why can t a thin astigmatic lens be used as an anamorphic lens

The way to correct astigmatism is to use a lenamp that converges (or dishyverges) rays in one plane while not affecting rays in the perpendicular plane Such a lens is a cylindrical lens (Fig 65l which is curved in one direction but not in the pershypendicular direction as if cut out of a cylindemiddotr of glass (see the TRY IT) The ophthalmologist will then preshyscribe a certain amount of cylindrishycal curvature to your glasses specishyfying the orientation along which the cylinder is to lie Such astigmashytism may be concurrent with an overall myopia say In that case your prescription may have a sphershyical component of - 2 5 diopters and a cylindrical component of -075 diopters at a 100 orientation

FIGURE 65

Cylindrical lens Rays 7 and 2 in the horizontal plane are made to converge Rays 3 and 4 in the vertical plane are essentially unaffected

It has been suggested that El Greco had severe astigmatism which would make the world look elongated to him and that this is why he painted the elongated figshyures for which he is famous This is really no explanation His astigmashytism would have also made his paintings look elongated and his figures would have looked to him to be the same shape as his models only if they were in fact the same shape

TRY IT

FOR SECTON 628

A cylindrical lens

As described in the first TRY IT for Section 34A you can make a cylindrical lens by filling a straight-sided cylindrical jar with water Fill the jar about half full with water put the lid gn tightly and hold the jar on its side The top surface of the water is then the flat side of a plano-convex iens and the bottom (cuNed) surface is the convex side Hold the lens about t m above this page and look down through it at the print Keeping the lens still rotate the page Also try this with a pencil as the object instead of this page Try to ignore any wobbles due to nonuniformity of the glass You now have some idea of what an astigmatic eye sees

Hold the lens about 1 m above a piece of graph paper (or any crosshatched paper) with the length of the jar oriented parallel to one set of lines With your eyes close to the lens look down through the lens at the graph paper What happens to the lines running

parallel to the jar To the perpendicular set of lines Why

Use your lens to try to focus a line image of the sun (when it is overhead) or a high lightbulb onto a piece of paper Move the lens up or down until you have made the line as sharp as you can then measumiddotre its distance to the paper (the focal length of the cylindrical lens) in meters Determine the power of the lens in diopters If the jar had a larger diameter would the power be greater or smaller Find another jar and try it

C Contact lenses

Contact lenses correct viSion in essentially the same manner as glasses but they do have a few opshytical differences These lenses are worn in contact with the cornea hence the name The eye then sees the image at the same angle (detershymined by the central ray) as it would see the object without the lens so the image on the retina is the same size in either case In the case with eyeglasses the eye is at some distance from the lens so the image appears a different size than the object (Hold a lens from your glasses or a contact lens a few inches from your eye and look at an object that extends beyond the lens so you can compare object and image sizes)

PON DER

Why does the converging lens cause the image to look larger Try ray tracing using two lenses one to represent the converging lens and one to represent the lens of your eye

This magnification (for the hypershyopic eye) and shrinking (for the myshyopic eye) is generally inSignificant and rarely a reason to get contact lenses (When you first put on strong glasses the world may apshypear smaller or larger and seem to shift as you move your eyes Howshyever your brain soon compensates for this effect)

Whereas the orientation of the asshytigmatic correction in an eyeglass is important a spherical contact lens can correct for astigmatism even

62 SIlVGLEmiddotLENS IlVSTRUMENTS

without remaining In a single orishyentation The reason for this is that the contact lens the cornea and the tear fluid that fills the space beshytween them all have about the same index of refraction The only bendshying of light therefore occurs at the front surface of the contact lens (Fig 66) Since this surface is spherical there will be no astigmashytism (Soft contact lenses tend to be too flexible to correct astigmatism but hard contact lenses do It quite well)

Since your contact lens moves when your eye moves you cant look through different parts of the lens

FIGURE 66

(a) A contact lens on the cornea with tear fluid in between (b) Photograph of a contact lens

Fluid

Contac t lens

1--1-______ Cornea

(a)

163

for reading and for distant viewing as easily as you can with bifocal glasses However when you look down suffiCiently the motion of the contact lens is stopped by the lower lid so the contact lens slips on the cornea Bifocal contact lenses take advantage of this fact The outer part of the lens which is located over the pupil when you look down has a different curvature or index of refraction than the center of the lens (which is normally over the pushypil and which will return to that position when you look up in order to resume its tight fit to your corshynea)

D The magnifying glass

We have argued that if you place your eye immediately behind a conshyverging lens (which well see is a magnifying glass) the image apshypears the same size as the object did without the lens (see Fig 63d) One often sees movie detectives holding the magnifying glass at arms length In that case the image does appear larger than the object Nevertheless this is not the best way to hold the magnifying glass To get the largest image on your retina you should place your eye close to the magnifying glass at which distance the magnifying glass does not magnify The explashy

(b)

nation of this paradoxical stateshyment depends on the fact that the magnifying glass enables you to bring Objects very close to your eye and still keep them in focus The objects look big because being close they subtend a large angle Without the magnifying glass you would have to move the objects farshyther away in order to focus sharply on them and thus would have a smaller image on your retina

Lets see how this works In Figshyure 67a the object is located at the normal eyes near point 25 cm The image on the retina is shown its loshycation determined by the central ray alone (since we know the eye will focus It on the retina) In Figure 67b a larger retinal image Is obshytained with a magnifying glass (of focal length less than 25 cm) Here the object is located at the focal point of the lens and consequently the rays leaving the magnifying glass are parallel to each other as they enter the eye Such rays are foshycused by the relaxed eye Again the central ray locates the Image on the retina Because the object is closer the central ray makes a bigger angle with the axis in Figure 67b than in Figure 67a so the retinal image is larger The magnifying glass has done its job (The TRY IT suggests several ways to make a magnifying glass)

The magnification or magnifyshying p ower of a lens is usually given as the ratio of the image sizes in these two sltuttions (ie with and without the magnifying glass) which is equal to the ratio of the object distances

Magnifying power = 25ft (f in em)

For example iff = 100 mm = 10 cm the magnifying lens has magshynifying power of N = 25 This is written as 25X (and read as 25 power)

You can get somewhat greater magnification If you place the object closer than the focal point at the point where it forms a virtual image 25 cm from the eye (Fig 67c) Your eye can focus on this virtual image by accommodating which is more tiring than viewing with parallel

CHAPTER 6 OPTICAL INSTRUMENTS

164

Lens of

Objec t

Image

1~~~---------Retina

(a)

Magnifying

glass Lens of

Image

bullbull Object

~____ f __--I~

Retina

(b)

eye

- ----shy - shy - - -- shy

25 cm------------~

Magnifying Lens of Virtual glass eye image

- ------ ----- - - - -- shyImage

I ~1~~------------ 25 cm-------~ Retina

(e)

to make it as close to the virtual imshyFIG URE 67

age as possible) (a) Unaided normal eye object at near The same principle can be appliedpoint (b) Eye with magnifying glass to a camera for close-up photograshyimage at infinity (c) Eye with magnifying

phy A close-up lens is nothing butglass image at 25 cm Note the relative sizes of the images on the retinas The a magnifying glass Placed in front compound lens of the eye is treated as a of the camera lens it allows the thin lens in this figure camera to focus on very close obshy

jects Just as with the eye the camshyrays but does give a bigger retinal era actually focuses on the virtual image than that obtained in Figure image produced by the magnifying 67b The magnification is then glass For example if you place the larger (by 1) than the nominal magshy object at the focal point of the magshynifying power given by the formula nifying glass you should set the above (So our 25X magnifier acshy camera to focus at infinity tually magnifies 35 times used In principle by using a very short this way Of course you want the focal length lens you can make the eye as close to the lens as possible image on your retina (or film) as

large as you like Generally howshyever the aberrations become too large for magnifications much beshyyond 5X Weve seen tha t assuming enough light is available we can reshyduce aberrations by stopping down or using a smaller diameter lens This is just what van Leeuwenhoek (1632-1723) did with his pioneershying mic roscopes his lenses were pinhea d size ground with incredishyble skill and had focal lengths as short as I mm giving a magnifyshying power of 200 With good lightshying and careful mounting of such a tiny lens and the specimen he could see spermatozoa and other wee animals He opened up the world of microscopy with a microshyscope whose entire size was about two inches Modern microscopes are bigger and compound-they use more (han one lens It is interesting to note that the compound microshyscope was invented before Leeuwenshyhoek was born but his lenses were so far superior to the competition that he could do better with a simshyple magnifying glass

TRY IT

FOR SECTION 620

A water magnifying glass

If you have a spherical glass bottle you can make a thick lens by filling it with water (Secs 34A and 348) or make a plano-convex lens as in the TRY IT for Section 628 (One of the attractions of a wine glass besides its content is that the spherical lens formed by the wine in the round-bottom glass creates on the table cloth images of nearby candles The next time you re served wine while pretending to judge its color like a true connoisseur look through the wine at the inverted image of the room ) Spherical glass-bottle lenses were used to concentrate the light of a candle on fine work such as lace making (Fig 68) Such a lace-makers condenser was described by John White in 7657 under the heading How to make a glorious light with a candle like sunshine Round bottles of water left in an open window have been known to start fires when the

63 COMPOUND MICROSCOPES

165

fiGURE 68

Lacemakers condenser capable of focusing the light of a candle on the work of the lacemaker

sun moved into the right position In Jules Vernes Mysterious Island the heroes who are stranded on a desert island without matches (of course) make a lens by holding water between the glasses from two pocket watches The lens is then used as a burning glass to start a fire

A water droplet that makes a nice lens can be formed with an eyedropper If you hold the drop in front of a printed page you should be able to measure its focal length-roughly the greatest distance from the page that you can hold the drop and still see an erect image (You may have to examine the image with another magnifying glass) Your drop will probably be bigger than Leeuwenhoeks lenses so youll get some idea of the viewing problems he had (You can also measure the focal length by the method of the TRY IT for Sec 348)

To hold a slightly larger droplet pierce a piece of aluminum foil with the tip of a pencil and rotate the pencil making a reasonab ly round hole about 5 mm in diameter Pour a little water over the hole in the foil to form a droplet of water across it that can be used as a magnifying glass (Alternatively a wire loop of the same diameter can be used) Looking through the droplet you can estimate its

focal length and magnification power Th e focal length should be quite small (about 75 cm which means a 76X magnifier)

A way to make a larger water lens is to freeze the water in the bottom of a spherically shaped bowl The water will freeze from the outside inward and concentrate the less easily frozen impurities on the inside as well as developing bumps and cracks as it freezes leaving you with a rather foggy lens that scatters the light instead of focusing it If you freeze the water slowly and take it out of the freezer before the last bit of water is frozen you can get a reasonably clear lens In the short time before your ice lens drips all over everything you should be able to verify that it is a magnifying glass and make some estimates of its magnifying power and focal length It is very hard to get any kind of decent image from an ice lens but you may be able to concentrate the suns rays enough to use the lens as a burning glass as Richard Adams describes in The Girl in a Swing

You dont know about the ice-bum Ill tell you Sometimes in the North in winter the iceJorms rtght across the curved top oj a hill Then when the sun shines the ice becomes like a magnifying glass so that the sun bums off all the grass and heather undemeath Later the ice melts and all through sprtng the hills bare until the grass grows again Dont you see the ice is what burns-the last thing youd expect to burn anything and yet it does

6 3 COMPOUND MICROSCOPES

The compound microscope uses a magnifying glass not to look dishyrectly at the object but rather to look at a real image created by anshyother lens Consider the Simplified compound microscope shown in Figure 69a (The TRY IT at the end of Sec 64B tells you how to make one) The first lens called the obshyjective because it is closest to the object PQ forms a real image PQ the intermediate image The viewer looks at this real image with a magshynifying glass called the eyepiece or ocular For viewing with relaxed eye muscles the rays leaving the eyepiece should be parallel to one another This means that the ~yeshypiece should be located at its focal distancefe from the intermediate image (see the figure and the imshyportant note in its caption) In orshyder to eliminate any stray light the two lenses are encased in the ends of a tube Sometimes a calibrated length scale called a graticule is drawn on a thin glass disk located in the plane of the intermediate imshyage This allows measurement of the size of objects observed in the microscope

Both lenses then provide magshynification As with any magnifying glass the shorter the focallengthfe the greater the magnification of the eyepiece The magnification of the objective is determined by the intershymediate image size PQ compared to the Object size PQ The location of the intermediate image is fixed because it must be at the focal point of the eyepiece and the spacshying between the lenses is usually fixed at about 18 cm so the viewers eye can be at a convenient height above the work table You can see by examining the central ray 2 that a larger image at that lecation means the object must be closer to the objective This can be accomshyplished with a smaller objective foshycallengthJo (Fig 69b) That is for larger magnification we want both

10 andfe smaller For the same diameter a smaller

62 SIlVGLEmiddotLENS IlVSTRUMENTS

without remaining In a single orishyentation The reason for this is that the contact lens the cornea and the tear fluid that fills the space beshytween them all have about the same index of refraction The only bendshying of light therefore occurs at the front surface of the contact lens (Fig 66) Since this surface is spherical there will be no astigmashytism (Soft contact lenses tend to be too flexible to correct astigmatism but hard contact lenses do It quite well)

Since your contact lens moves when your eye moves you cant look through different parts of the lens

FIGURE 66

(a) A contact lens on the cornea with tear fluid in between (b) Photograph of a contact lens

Fluid

Contac t lens

1--1-______ Cornea

(a)

163

for reading and for distant viewing as easily as you can with bifocal glasses However when you look down suffiCiently the motion of the contact lens is stopped by the lower lid so the contact lens slips on the cornea Bifocal contact lenses take advantage of this fact The outer part of the lens which is located over the pupil when you look down has a different curvature or index of refraction than the center of the lens (which is normally over the pushypil and which will return to that position when you look up in order to resume its tight fit to your corshynea)

D The magnifying glass

We have argued that if you place your eye immediately behind a conshyverging lens (which well see is a magnifying glass) the image apshypears the same size as the object did without the lens (see Fig 63d) One often sees movie detectives holding the magnifying glass at arms length In that case the image does appear larger than the object Nevertheless this is not the best way to hold the magnifying glass To get the largest image on your retina you should place your eye close to the magnifying glass at which distance the magnifying glass does not magnify The explashy

(b)

nation of this paradoxical stateshyment depends on the fact that the magnifying glass enables you to bring Objects very close to your eye and still keep them in focus The objects look big because being close they subtend a large angle Without the magnifying glass you would have to move the objects farshyther away in order to focus sharply on them and thus would have a smaller image on your retina

Lets see how this works In Figshyure 67a the object is located at the normal eyes near point 25 cm The image on the retina is shown its loshycation determined by the central ray alone (since we know the eye will focus It on the retina) In Figure 67b a larger retinal image Is obshytained with a magnifying glass (of focal length less than 25 cm) Here the object is located at the focal point of the lens and consequently the rays leaving the magnifying glass are parallel to each other as they enter the eye Such rays are foshycused by the relaxed eye Again the central ray locates the Image on the retina Because the object is closer the central ray makes a bigger angle with the axis in Figure 67b than in Figure 67a so the retinal image is larger The magnifying glass has done its job (The TRY IT suggests several ways to make a magnifying glass)

The magnification or magnifyshying p ower of a lens is usually given as the ratio of the image sizes in these two sltuttions (ie with and without the magnifying glass) which is equal to the ratio of the object distances

Magnifying power = 25ft (f in em)

For example iff = 100 mm = 10 cm the magnifying lens has magshynifying power of N = 25 This is written as 25X (and read as 25 power)

You can get somewhat greater magnification If you place the object closer than the focal point at the point where it forms a virtual image 25 cm from the eye (Fig 67c) Your eye can focus on this virtual image by accommodating which is more tiring than viewing with parallel

CHAPTER 6 OPTICAL INSTRUMENTS

164

Lens of

Objec t

Image

1~~~---------Retina

(a)

Magnifying

glass Lens of

Image

bullbull Object

~____ f __--I~

Retina

(b)

eye

- ----shy - shy - - -- shy

25 cm------------~

Magnifying Lens of Virtual glass eye image

- ------ ----- - - - -- shyImage

I ~1~~------------ 25 cm-------~ Retina

(e)

to make it as close to the virtual imshyFIG URE 67

age as possible) (a) Unaided normal eye object at near The same principle can be appliedpoint (b) Eye with magnifying glass to a camera for close-up photograshyimage at infinity (c) Eye with magnifying

phy A close-up lens is nothing butglass image at 25 cm Note the relative sizes of the images on the retinas The a magnifying glass Placed in front compound lens of the eye is treated as a of the camera lens it allows the thin lens in this figure camera to focus on very close obshy

jects Just as with the eye the camshyrays but does give a bigger retinal era actually focuses on the virtual image than that obtained in Figure image produced by the magnifying 67b The magnification is then glass For example if you place the larger (by 1) than the nominal magshy object at the focal point of the magshynifying power given by the formula nifying glass you should set the above (So our 25X magnifier acshy camera to focus at infinity tually magnifies 35 times used In principle by using a very short this way Of course you want the focal length lens you can make the eye as close to the lens as possible image on your retina (or film) as

large as you like Generally howshyever the aberrations become too large for magnifications much beshyyond 5X Weve seen tha t assuming enough light is available we can reshyduce aberrations by stopping down or using a smaller diameter lens This is just what van Leeuwenhoek (1632-1723) did with his pioneershying mic roscopes his lenses were pinhea d size ground with incredishyble skill and had focal lengths as short as I mm giving a magnifyshying power of 200 With good lightshying and careful mounting of such a tiny lens and the specimen he could see spermatozoa and other wee animals He opened up the world of microscopy with a microshyscope whose entire size was about two inches Modern microscopes are bigger and compound-they use more (han one lens It is interesting to note that the compound microshyscope was invented before Leeuwenshyhoek was born but his lenses were so far superior to the competition that he could do better with a simshyple magnifying glass

TRY IT

FOR SECTION 620

A water magnifying glass

If you have a spherical glass bottle you can make a thick lens by filling it with water (Secs 34A and 348) or make a plano-convex lens as in the TRY IT for Section 628 (One of the attractions of a wine glass besides its content is that the spherical lens formed by the wine in the round-bottom glass creates on the table cloth images of nearby candles The next time you re served wine while pretending to judge its color like a true connoisseur look through the wine at the inverted image of the room ) Spherical glass-bottle lenses were used to concentrate the light of a candle on fine work such as lace making (Fig 68) Such a lace-makers condenser was described by John White in 7657 under the heading How to make a glorious light with a candle like sunshine Round bottles of water left in an open window have been known to start fires when the

63 COMPOUND MICROSCOPES

165

fiGURE 68

Lacemakers condenser capable of focusing the light of a candle on the work of the lacemaker

sun moved into the right position In Jules Vernes Mysterious Island the heroes who are stranded on a desert island without matches (of course) make a lens by holding water between the glasses from two pocket watches The lens is then used as a burning glass to start a fire

A water droplet that makes a nice lens can be formed with an eyedropper If you hold the drop in front of a printed page you should be able to measure its focal length-roughly the greatest distance from the page that you can hold the drop and still see an erect image (You may have to examine the image with another magnifying glass) Your drop will probably be bigger than Leeuwenhoeks lenses so youll get some idea of the viewing problems he had (You can also measure the focal length by the method of the TRY IT for Sec 348)

To hold a slightly larger droplet pierce a piece of aluminum foil with the tip of a pencil and rotate the pencil making a reasonab ly round hole about 5 mm in diameter Pour a little water over the hole in the foil to form a droplet of water across it that can be used as a magnifying glass (Alternatively a wire loop of the same diameter can be used) Looking through the droplet you can estimate its

focal length and magnification power Th e focal length should be quite small (about 75 cm which means a 76X magnifier)

A way to make a larger water lens is to freeze the water in the bottom of a spherically shaped bowl The water will freeze from the outside inward and concentrate the less easily frozen impurities on the inside as well as developing bumps and cracks as it freezes leaving you with a rather foggy lens that scatters the light instead of focusing it If you freeze the water slowly and take it out of the freezer before the last bit of water is frozen you can get a reasonably clear lens In the short time before your ice lens drips all over everything you should be able to verify that it is a magnifying glass and make some estimates of its magnifying power and focal length It is very hard to get any kind of decent image from an ice lens but you may be able to concentrate the suns rays enough to use the lens as a burning glass as Richard Adams describes in The Girl in a Swing

You dont know about the ice-bum Ill tell you Sometimes in the North in winter the iceJorms rtght across the curved top oj a hill Then when the sun shines the ice becomes like a magnifying glass so that the sun bums off all the grass and heather undemeath Later the ice melts and all through sprtng the hills bare until the grass grows again Dont you see the ice is what burns-the last thing youd expect to burn anything and yet it does

6 3 COMPOUND MICROSCOPES

The compound microscope uses a magnifying glass not to look dishyrectly at the object but rather to look at a real image created by anshyother lens Consider the Simplified compound microscope shown in Figure 69a (The TRY IT at the end of Sec 64B tells you how to make one) The first lens called the obshyjective because it is closest to the object PQ forms a real image PQ the intermediate image The viewer looks at this real image with a magshynifying glass called the eyepiece or ocular For viewing with relaxed eye muscles the rays leaving the eyepiece should be parallel to one another This means that the ~yeshypiece should be located at its focal distancefe from the intermediate image (see the figure and the imshyportant note in its caption) In orshyder to eliminate any stray light the two lenses are encased in the ends of a tube Sometimes a calibrated length scale called a graticule is drawn on a thin glass disk located in the plane of the intermediate imshyage This allows measurement of the size of objects observed in the microscope

Both lenses then provide magshynification As with any magnifying glass the shorter the focallengthfe the greater the magnification of the eyepiece The magnification of the objective is determined by the intershymediate image size PQ compared to the Object size PQ The location of the intermediate image is fixed because it must be at the focal point of the eyepiece and the spacshying between the lenses is usually fixed at about 18 cm so the viewers eye can be at a convenient height above the work table You can see by examining the central ray 2 that a larger image at that lecation means the object must be closer to the objective This can be accomshyplished with a smaller objective foshycallengthJo (Fig 69b) That is for larger magnification we want both

10 andfe smaller For the same diameter a smaller

CHAPTER 6 OPTICAL INSTRUMENTS

164

Lens of

Objec t

Image

1~~~---------Retina

(a)

Magnifying

glass Lens of

Image

bullbull Object

~____ f __--I~

Retina

(b)

eye

- ----shy - shy - - -- shy

25 cm------------~

Magnifying Lens of Virtual glass eye image

- ------ ----- - - - -- shyImage

I ~1~~------------ 25 cm-------~ Retina

(e)

to make it as close to the virtual imshyFIG URE 67

age as possible) (a) Unaided normal eye object at near The same principle can be appliedpoint (b) Eye with magnifying glass to a camera for close-up photograshyimage at infinity (c) Eye with magnifying

phy A close-up lens is nothing butglass image at 25 cm Note the relative sizes of the images on the retinas The a magnifying glass Placed in front compound lens of the eye is treated as a of the camera lens it allows the thin lens in this figure camera to focus on very close obshy

jects Just as with the eye the camshyrays but does give a bigger retinal era actually focuses on the virtual image than that obtained in Figure image produced by the magnifying 67b The magnification is then glass For example if you place the larger (by 1) than the nominal magshy object at the focal point of the magshynifying power given by the formula nifying glass you should set the above (So our 25X magnifier acshy camera to focus at infinity tually magnifies 35 times used In principle by using a very short this way Of course you want the focal length lens you can make the eye as close to the lens as possible image on your retina (or film) as

large as you like Generally howshyever the aberrations become too large for magnifications much beshyyond 5X Weve seen tha t assuming enough light is available we can reshyduce aberrations by stopping down or using a smaller diameter lens This is just what van Leeuwenhoek (1632-1723) did with his pioneershying mic roscopes his lenses were pinhea d size ground with incredishyble skill and had focal lengths as short as I mm giving a magnifyshying power of 200 With good lightshying and careful mounting of such a tiny lens and the specimen he could see spermatozoa and other wee animals He opened up the world of microscopy with a microshyscope whose entire size was about two inches Modern microscopes are bigger and compound-they use more (han one lens It is interesting to note that the compound microshyscope was invented before Leeuwenshyhoek was born but his lenses were so far superior to the competition that he could do better with a simshyple magnifying glass

TRY IT

FOR SECTION 620

A water magnifying glass

If you have a spherical glass bottle you can make a thick lens by filling it with water (Secs 34A and 348) or make a plano-convex lens as in the TRY IT for Section 628 (One of the attractions of a wine glass besides its content is that the spherical lens formed by the wine in the round-bottom glass creates on the table cloth images of nearby candles The next time you re served wine while pretending to judge its color like a true connoisseur look through the wine at the inverted image of the room ) Spherical glass-bottle lenses were used to concentrate the light of a candle on fine work such as lace making (Fig 68) Such a lace-makers condenser was described by John White in 7657 under the heading How to make a glorious light with a candle like sunshine Round bottles of water left in an open window have been known to start fires when the

63 COMPOUND MICROSCOPES

165

fiGURE 68

Lacemakers condenser capable of focusing the light of a candle on the work of the lacemaker

sun moved into the right position In Jules Vernes Mysterious Island the heroes who are stranded on a desert island without matches (of course) make a lens by holding water between the glasses from two pocket watches The lens is then used as a burning glass to start a fire

A water droplet that makes a nice lens can be formed with an eyedropper If you hold the drop in front of a printed page you should be able to measure its focal length-roughly the greatest distance from the page that you can hold the drop and still see an erect image (You may have to examine the image with another magnifying glass) Your drop will probably be bigger than Leeuwenhoeks lenses so youll get some idea of the viewing problems he had (You can also measure the focal length by the method of the TRY IT for Sec 348)

To hold a slightly larger droplet pierce a piece of aluminum foil with the tip of a pencil and rotate the pencil making a reasonab ly round hole about 5 mm in diameter Pour a little water over the hole in the foil to form a droplet of water across it that can be used as a magnifying glass (Alternatively a wire loop of the same diameter can be used) Looking through the droplet you can estimate its

focal length and magnification power Th e focal length should be quite small (about 75 cm which means a 76X magnifier)

A way to make a larger water lens is to freeze the water in the bottom of a spherically shaped bowl The water will freeze from the outside inward and concentrate the less easily frozen impurities on the inside as well as developing bumps and cracks as it freezes leaving you with a rather foggy lens that scatters the light instead of focusing it If you freeze the water slowly and take it out of the freezer before the last bit of water is frozen you can get a reasonably clear lens In the short time before your ice lens drips all over everything you should be able to verify that it is a magnifying glass and make some estimates of its magnifying power and focal length It is very hard to get any kind of decent image from an ice lens but you may be able to concentrate the suns rays enough to use the lens as a burning glass as Richard Adams describes in The Girl in a Swing

You dont know about the ice-bum Ill tell you Sometimes in the North in winter the iceJorms rtght across the curved top oj a hill Then when the sun shines the ice becomes like a magnifying glass so that the sun bums off all the grass and heather undemeath Later the ice melts and all through sprtng the hills bare until the grass grows again Dont you see the ice is what burns-the last thing youd expect to burn anything and yet it does

6 3 COMPOUND MICROSCOPES

The compound microscope uses a magnifying glass not to look dishyrectly at the object but rather to look at a real image created by anshyother lens Consider the Simplified compound microscope shown in Figure 69a (The TRY IT at the end of Sec 64B tells you how to make one) The first lens called the obshyjective because it is closest to the object PQ forms a real image PQ the intermediate image The viewer looks at this real image with a magshynifying glass called the eyepiece or ocular For viewing with relaxed eye muscles the rays leaving the eyepiece should be parallel to one another This means that the ~yeshypiece should be located at its focal distancefe from the intermediate image (see the figure and the imshyportant note in its caption) In orshyder to eliminate any stray light the two lenses are encased in the ends of a tube Sometimes a calibrated length scale called a graticule is drawn on a thin glass disk located in the plane of the intermediate imshyage This allows measurement of the size of objects observed in the microscope

Both lenses then provide magshynification As with any magnifying glass the shorter the focallengthfe the greater the magnification of the eyepiece The magnification of the objective is determined by the intershymediate image size PQ compared to the Object size PQ The location of the intermediate image is fixed because it must be at the focal point of the eyepiece and the spacshying between the lenses is usually fixed at about 18 cm so the viewers eye can be at a convenient height above the work table You can see by examining the central ray 2 that a larger image at that lecation means the object must be closer to the objective This can be accomshyplished with a smaller objective foshycallengthJo (Fig 69b) That is for larger magnification we want both

10 andfe smaller For the same diameter a smaller

63 COMPOUND MICROSCOPES

165

fiGURE 68

Lacemakers condenser capable of focusing the light of a candle on the work of the lacemaker

sun moved into the right position In Jules Vernes Mysterious Island the heroes who are stranded on a desert island without matches (of course) make a lens by holding water between the glasses from two pocket watches The lens is then used as a burning glass to start a fire

A water droplet that makes a nice lens can be formed with an eyedropper If you hold the drop in front of a printed page you should be able to measure its focal length-roughly the greatest distance from the page that you can hold the drop and still see an erect image (You may have to examine the image with another magnifying glass) Your drop will probably be bigger than Leeuwenhoeks lenses so youll get some idea of the viewing problems he had (You can also measure the focal length by the method of the TRY IT for Sec 348)

To hold a slightly larger droplet pierce a piece of aluminum foil with the tip of a pencil and rotate the pencil making a reasonab ly round hole about 5 mm in diameter Pour a little water over the hole in the foil to form a droplet of water across it that can be used as a magnifying glass (Alternatively a wire loop of the same diameter can be used) Looking through the droplet you can estimate its

focal length and magnification power Th e focal length should be quite small (about 75 cm which means a 76X magnifier)

A way to make a larger water lens is to freeze the water in the bottom of a spherically shaped bowl The water will freeze from the outside inward and concentrate the less easily frozen impurities on the inside as well as developing bumps and cracks as it freezes leaving you with a rather foggy lens that scatters the light instead of focusing it If you freeze the water slowly and take it out of the freezer before the last bit of water is frozen you can get a reasonably clear lens In the short time before your ice lens drips all over everything you should be able to verify that it is a magnifying glass and make some estimates of its magnifying power and focal length It is very hard to get any kind of decent image from an ice lens but you may be able to concentrate the suns rays enough to use the lens as a burning glass as Richard Adams describes in The Girl in a Swing

You dont know about the ice-bum Ill tell you Sometimes in the North in winter the iceJorms rtght across the curved top oj a hill Then when the sun shines the ice becomes like a magnifying glass so that the sun bums off all the grass and heather undemeath Later the ice melts and all through sprtng the hills bare until the grass grows again Dont you see the ice is what burns-the last thing youd expect to burn anything and yet it does

6 3 COMPOUND MICROSCOPES

The compound microscope uses a magnifying glass not to look dishyrectly at the object but rather to look at a real image created by anshyother lens Consider the Simplified compound microscope shown in Figure 69a (The TRY IT at the end of Sec 64B tells you how to make one) The first lens called the obshyjective because it is closest to the object PQ forms a real image PQ the intermediate image The viewer looks at this real image with a magshynifying glass called the eyepiece or ocular For viewing with relaxed eye muscles the rays leaving the eyepiece should be parallel to one another This means that the ~yeshypiece should be located at its focal distancefe from the intermediate image (see the figure and the imshyportant note in its caption) In orshyder to eliminate any stray light the two lenses are encased in the ends of a tube Sometimes a calibrated length scale called a graticule is drawn on a thin glass disk located in the plane of the intermediate imshyage This allows measurement of the size of objects observed in the microscope

Both lenses then provide magshynification As with any magnifying glass the shorter the focallengthfe the greater the magnification of the eyepiece The magnification of the objective is determined by the intershymediate image size PQ compared to the Object size PQ The location of the intermediate image is fixed because it must be at the focal point of the eyepiece and the spacshying between the lenses is usually fixed at about 18 cm so the viewers eye can be at a convenient height above the work table You can see by examining the central ray 2 that a larger image at that lecation means the object must be closer to the objective This can be accomshyplished with a smaller objective foshycallengthJo (Fig 69b) That is for larger magnification we want both

10 andfe smaller For the same diameter a smaller