L-6 THE EYE

1. PURPOSE:

To investigate the eye, considered as an optical instrument. Several specific measurement tasks include: (1) Measurement of the pupil size in the dark and bright adapted eye, (2) Measurement of the time delay of visual signals from dim light.

2. APPARATUS:

Small penlight flashlight.
Victorian style stereoscope with view cards.
Modern stereo viewers with 3D transparencies.
Aerial photo viewer, with examples.
Various color filters, or colored cellophane.
Pinholes, or materials for making pinholes.
Set of optician's lenses.
Ophthalmoscope (if available).
Examples of other kinds of stereo pictures and viewers.
Pulfrich pendulum set-up, with neutral density filters.
NBS resolution chart.
Chart: Fundus of the Human Eye. American Optometric Association
Chart of Optical Constants for a Standard Eye. Military Standardization Handbook

3. REFERENCES:

Begbie, G. Hugh. Seeing and the Eye, An Introduction to Vision. Anchor Press/Doubleday, 1973.

Coletta, Vincent P. College Physics. Mosby, 1995. Chapter 25, "The Eye and Optical Instruments."

Cornsweet, Tom. N. Visual Perception. Academic Press, 1970.

Julesz, Bela. Foundations of Cyclopean perception. U. of Chicago Press, 1971.

Kaufman, Lloyd. Sight and Mind, an introduction to visual perception. Oxford, 1974.

Palmer, C. Harvey. Optics Experiments and Demonstrations. John Hopkins University Press, 1962. Particularly Experiment A18. "Some properties of the human eye" written in collaboration with Leonard Matin.

Walker, Jearl. The Flying Circus of Physics, with answers. Wiley, 1977.

While some background and theory is given in the text below, the student should read everything about the eye in a standard physics textbook before undertaking these exercises.

4. EYE ANATOMY AND THE STANDARD EYE:

Fig. 1. The anatomy of the human eye.

Fig. 1. shows the major structural elements of the eye. there's considerable variation in eyes in the human population. Some people are born with eye defects, and some people require glasses at an early age. However, those who study the eye have constructed a reference for comparison, the standard eye. See: Military Standardization Handbook, p. 4.2 - Optical constants for a standard eye.

Fig. 2. Horizontal cross section of the right eye.

Material         n =

Aqueous humor    1.226
Vitreous humor   1.337
Cornea           1.376
Lens             1.42
Water            1.33

The transparent "fluids" in the eye have about the same index of refraction as water. This should be no surprise, as most of the body is water.

The refractive indices are not uniform. The outer edge of the lens has an index of 1.386, its center has an index of 1.46, for an effective average index of 1.42.

The optical power of the eye is mostly at the interface between the outside air and the cornea. (1) Most of the refraction occurs at the cornea, because of its curvature, and the large difference in the index of refraction between it and the surrounding air. The lens of the eye provides an additional (but adjustable) lens power.

Lens     Power in    Variation
element  diopters    in diopters  

Cornea   43          38-48
Lens     19          17-26
Total    58.6

Eyeball size, front to back: 2.475 cm

Cornea radius, outer: 0.798 cm

Cornea radius, inner: 0.622 cm

The `effective' location of the optical system of the eye is about 7.5 mm behind the front surface of the cornea. This is about 17.25 mm in front of the retina. For some purposes a simplified model called the reduced eye is used. It is a sphere 24mm in diameter, with an optical center located 16mm in front of the retina. See Coletta, p. 708.

Note: while there is much physics and chemistry in the visual process, the study of vision encompasses physiology and neuroscience. It is an active area of research in which there's more information and puzzling phenomena than definitive answers. Many of the hypotheses and models now tentatively accepted will surely be modified by future research.

5. THE BLIND SPOT:

Many people don't realize they have a blind spot. (2) Actually they have two of them, one in each eye. The point at the back of the eyeball where the optic nerve bundle enters is deficient in light receptors, both rods and cones, and therefore is a blind spot surrounded by the retina. It is displaced about 3mm from the optic axis. You can convince yourself of this by looking at the following picture with one eye covered.

Fig. 3. Test for the blind spot.

Cover your right eye and look directly at the X with your left eye. Move closer or farther from the page until the O disappears. What has happened is that the image of the O falls directly on the blind spot. This indicates that the image of the O must be on the nasal side of the retina of your left eye. If this is so, and your body is reasonably symmetric, you should be able to find the blind spot in your right eye. Look at the O with your right eye, covering your left eye. Move until the X disappears.

Using the reduced eye model, the angle between the O and X at which one disappears should be about q = 3mm/16mm = 0.19 radian. Do your experiments with Fig. 2 confirm this?

Notice how complete the disappearance is, even though the O and X are quite large. Estimate the angular diameter of the blind spot. This exercise may be done with a ruler held horizontally. Look at one of the numbers marking inches, and see which other number disappears.

Question 1: The blind spots can never coincide in two-eyed vision. That is, a small object you are looking at can never simultaneously produce an image on the blind spot of both eyes. Explain.

6. FLOATERS:

Appearance of floaters
against a blue sky.
Photoshop simulation.

The fluids in the eye have long protein molecules. Sometimes these clump together so they cast a diffraction pattern on the retina, and therefore can be seen. They are best seen when looking at a featureless white background. If they are not centered in your field of view, you may try to move your eyes 'toward them' to see them better. That won't work, because they move with the eye, and though you may 'jostle' them a bit, you can't make them come to the center of vision.

With advancing age the network of collagen within the Vitreous humor begins to shrink and pull away from the back of the eyeball. During this process you may be more conscious of floaters, and of dark patches of clumped collagen blocking light from the retina. Sometimes this process is too rapid, and one sees flashes of light at the retina where the collagen is being pulled away. This may be a signal that the retina itself is detaching from the eyeball, a situation that indicates you should see a doctor immediately! Such detachment can occur from blows to the head. If caught soon enough, detached retinas can usually be reattached successfully with the aid of lasers to cauterize a few spots on the retina.

Fig. 4. Retinal inversion demo,
from Columbus' Egg.
Inset shows what the viewer sees
when looking at the nearby pin.

Another factor that can contribute to retinal detachment is weak spots or holes in the retina, allowing vitreous humor to leak behind the retina.

Look at a featureless background and see whether you can see any floaters in your own eye. Do not be alarmed if you see some small ones, for they are common.

7. INVERSION OF THE RETINAL IMAGE:

You have often heard that the retinal image is inverted, and you are easily convinced of that by looking at the diagrams of eye anatomy (Figs. 1 and 2). But have you ever wondered how you could get more direct evidence of that fact?

Use a brightly illuminated pinhole as a source, held about four inches from the eye. Hold a pin head between the pinhole and the eye. The pin is less than a focal length from the eye, so it cannot form a real image on the retina. It casts a shadow on the retina, which looks `wrong side up'.

Another method: This does not use the pin. Hold the pinhole closer to the eye than before. Close your eyelid, but not completely. You will see an upside down image of your eyelashes.

While you are playing with the pinhole, move it about constantly, and you may see the image of the shadow of the blood vessels on your retina. Section 11 of this experiment describes a more reliable method for seeing them.

8. THE FAR AND NEAR POINT OF THE EYE:

The far and near points of the eye are the farthest and nearest distances of objects for which the eye can produce a clear retinal image. For the `normal' eye the far point is infinity and the near point is about 25 cm. When looking at a featureless visual field, the eye focuses at about 1 meter (not infinity, as you might have expected) (3).

Fig. 5. Normal eye, relaxed,
object at infinity.

If you, or your lab partner, wear glasses, find out whether they correct for myopia (nearsightedness), or hyperopia (far-sightedness). Remember that diverging lenses correct near-sightedness, and converging lenses correct far-sightedness.

If you don't wear corrective lenses your near point should be about 25 cm. Check whether it is. Find someone who does wear glasses, and ask them what their near point is, and record that information. Now their eyeglasses should be of sufficient diopter rating that they form an image at 25 cm for an object at their near point. Check this on an optical bench, or by any other method. Is it approximately so?

The near point of myopic people is too close to the eye, closer than 25 cm. This is not an inconvenience, but the fact that the far point is also too close means that one cannot see distant objects clearly. Eyeglasses (diverging) to correct this should have a diopter rating such that they form a virtual image at infinity of an object at the eye's far point.

Fig. 6. Myopic eye, relaxed,
object at infinity.
Fig. 7. Myopic eye, relaxed,
with corrective lens,
object at infinity.

Corrective glasses for myopic eyes are divergent (negative) chosen so that objects at infinity can be clearly seen. If the eye has normal accommodation, this will also result in objects at 25 cm being clearly seen, with the corrective glasses.

Hyperopia (far-sightedness), is probably more annoying to a person than myopia, for the person cannot see nearby objects clearly, and while the hyperopic eye can focus `beyond infinity', that ability is useless in everyday life. Correction requires converging (positive) lenses to bring the far point to infinity, which should also bring the near point to about 25 cm.

Fig. 8. Hyperopic eye, focused
as close as possible.
Fig. 9. Hyperopic eye, with
corective lens, focused
as close as possible.

Presbyopia is the condition (usually due to advanced age, typically after age 40) in which the eye cannot focus over as wide a range of distances. The far point is closer, and the near point is farther, from the eye than for the normal eye of a young person. This is because the lens loses resiliency and/or the muscle that controls the lens loses its power to change its focal length. Thus we lose accommodation. This cannot be corrected by eyeglasses of a single power, so bifocal, or trifocal lenses are prescribed. (4)

If you are near- or far-sighted, experiment with corrective lenses to see whether you can determine your correct eyeglass prescription.

The near point depends upon the size of the eye's pupil, which acts as an aperture stop, and bright illumination causes the pupil to become smaller, improving the resolution. Try this by looking at something illuminated with a bright desk lamp.

You can artificially reduce the aperture stop of the eye by placing a pinhole in front of and close to the eye. This should make it possible for you to clearly see objects 3 or 4 cm from the pinhole! Could you use this method to see an object as close as 1 cm from the pinhole?

Laser tests of vision. An interesting phenomena of coherent light is the speckle pattern one sees when a laser beam is diverged onto a white screen, covering an area of, say 1 foot diameter. The illuminated screen seems to have a pattern tiny spots, dots, or speckles. You may be surprised to notice that this pattern of spots seems to move relative to the screen as you move your head. If you move your head right, and the pattern moves left, that means the pattern appears nearer than the screen. (5)

Your eye is creating the pattern, locating it in space where your eye most comfortably accommodates. If the pattern is nearer than the screen, you are near sighted. If it is farther away than the screen, you are far sighted. You can make this more precise by walking toward or away from the screen until the pattern is at the same distance as the screen. That distance is your distance of most comfortable accommodation

Experiment with low power lenses (both converging and diverging) in front of your eyes, so see how this alters the apparent location of the speckle pattern.

9. SPHERICAL ABERRATION: (6)

The refractive index of the eye lens is slightly greater at its center than at its margin and the spherical aberration of the eye is thus reduced. This aberration is not absent, however, as can be readily shown. Hold a card close to the eye and move its horizontal upper edge vertically across the path of the light rays entering the pupil from a distant horizontal straight edge such as the roof line of a building or even a cabinet across the room. As the card is moved upward the horizontal line of the object appears to shift upward as the card cuts off the paraxial rays leaving only the upper marginal rays. (7)

10. IRIS:

A part of the adaptation of the eye to low and high light levels is achieved by varying the diameter of the iris aperture. Its diameter is 8 mm when the eye is dark adapted, and may be as small as 2 or 3 mm diameter in bright light. Therefore its aperture area may vary by more than a factor of 10. The change in pupil diameter is slow enough (5 to 10 seconds, but full dilation may take up to 10 minutes) to be easily observed by looking directly at an incandescent bulb and then interposing a mirror between the bulb and the eye to see the pupil enlarge.

Both pupils respond together, and normally, under all lighting conditions, the pupils of both eyes will be the same size. Test this. While observing the pupil of one eye, cover and uncover the other eye with your hand. Hold a millimeter scale quite close to the eye and a mirror about five inches away to observe both the pupil and the millimeter scale. Make measurements of the pupil diameter at both high and low light levels.

No matter how hard you try, or how you stimulate your eyes with light, you cannot consciously make one pupil large and the other small. The brain is sending the same signal to the iris muscles of both eyes at once. Is that signal dependent on the eye receiving the most light, or the eye receiving the least light?

A telecentric lens system for
measuring objects at unknown distances.

A special, but simple, lens arrangement may be used to allow one person to measure the pupil diameter of another person. It is a telecentric lens, and is a nice example of physical optics applied to measurement. It correctly measures sizes even though the distance to the object being measured is unknown. The stop is at the focal point of S1, and there's a transparent measuring scale at the plane of the image. The image L2 and scale are viewed with lens L2.

11. BLOOD VESSELS ON THE RETINA:

The cornea and the lens have no direct blood supply, nor do the fluids in the eye. The retina is supplied by a branching network of (blood vessels) arterioles in front of the retina. This seems a rather poor design (8), since these blood vessels get in the way of the light reaching the retina. Fortunately they are small, and our brain learns to ignore them. However, when light enters the eye from an unusual direction, the blood vessels may cast shadows on the retina, which can be seen.

You may easily see these blood vessels with the aid of a small penlight flashlight. Remove the cover and lens from the bulb if possible. Close your eyes. Touch the light to your lower eyelid just at the edge of the bone of your eye socket. Do not press it forcefully against your eyeball! Now move the light around a small amount until you see a network of black lines that looks like a map of the Amazon River. This is the pattern of the blood vessels. It may quickly fade, due to retinal fatigue; that's why it helps to keep the light moving constantly. The light is entering directly through your skin and through the side of your eyeball.

You can identify the fovea very clearly as a spot in the center with no blood vessels leading into it. You can also see the blind spot where the blood vessels enter the eye. (Is it on the nasal or temporal side?) Also, when you see the blood vessels, open your eye half way to get a double exposure of the blood vessels onto the external world. You learn directly the meaning of foveation. (9) (Look it up.)

There are many medical applications where diagnoses can be made by use of light seen directly through tissues.

If one were designing an eye, it would seem better to put the blood vessels behind the retina, so they don't obscure vision. Indeed some sea animals have eyes constructed this way. Evolution doesn't produce the best adaptations, only `good enough' adaptations for an organism's survival.

12. RESOLUTION OF THE EYE:

The determination of the ability of the eye to distinguish small objects, or the separation of small objects near to each other, is not as simple as you'd think. A lot depends on how one defines `resolution' and `visual acuity'.

One limitation on resolution is the size of the pupil. The edges of the pupil produce a diffraction pattern around point images. The Rayleigh criterion says that two such images near each other will be resolved only when their angular separation is 1.22l/D where l is the wavelength of light and D is the diameter of the circular aperture stop. In bright light the eye's pupil diameter can be as small as 2 mm, so the Rayleigh criterion gives a resolution of 1.153' (' is the symbol for minute of arc. 60' = 1°).

But one would not expect the eye to do quite this well, for light scattering and lens and cornea defects further degrade the retinal image.

Schematic diagram of the array
of rods (small dots)
and cones (larger objects)
on the retina (From Cornsweet.)

Then there's the retina itself. The mosaic of light receptor cells on the retina consists of cells called `rods' that are not color sensitive, and `cones' of three types that are selectively color sensitive. The rods are the primary determiners of light sensitivity, but the cones (being more numerous and closely spaced) are more important in determining resolution, and are the only receptors that allow us to distinguish colors. At low light levels our vision is mainly from the rods, and therefore our ability to distinguish colors is poor in dim light.

These receptor cells are remarkably sensitive. Hecht et al. found that the visual system can detect a flash of light 60% of the time when it contains about 90 quanta. (10) Most of the incident quanta are lost on the way to the receptors: 3% are reflected from the cornea, about half of the rest are absorbed by pigment in the eye fluids. So only about 48% reach the retina. Of these, some fall on insensitive regions between the rods, some are scattered. Hecht et al. estimated that at a wavelength of 520 nm less than 20% of the quanta incident on the retina are actually absorbed by visual pigment in the rods. Subsequent studies have shown that the number of quanta absorbed by visual pigment at the threshold of vision is two, and that one quantum of light is sufficient to activate a rod. [This fact is no surprise to physicists, for we know from the physics of light that one quanta cannot activate two light receptors, and we know that light does activate a receptor.]

Many science trivia books of the `gee-whiz, isn't science amazing' variety, quote this last fact (2 quanta can be seen) without mentioning that the human eye as a system has only about 2% quantum efficiency. That is, it takes 90 quanta entering the eye to result in the two quanta that are `seen' (60% of the time). So the actual quantum efficiency is more like a bit over 1%.

In the retinal mosaic the cones have diameters of 3m and their centers are spaced about that far apart. Therefore they subtend about 35" arc. (At the very center of the fovea they can be as close as 20".) (11)

Yet, a fine, dark line subtending only 1" (one second of arc) width can be seen against a bright background. But the human eye cannot see a dark dot subtending 1", a dot must subtend at least 1' (1 minute of arc) to be seen. A line with width 1" must have length subtending about 30' to be seen. That is, the light must be distributed over 60 or 70 cones.

Your laboratory may have high quality standard lens testing grids available. See if you can use one to determine the limit of angular resolution of your eye.

Here's an easy way to measure visual acuity. (12) Draw two parallel lines 1 mm apart on a piece of paper. Tape the paper to the wall in a well illuminated room. Walk backwards from the wall until you cannot distinguish the two lines. Measure your distance from the wall. (Typical distance is about 4 meters). Then (1 mm)/(distance in mm) is your visual acuity in radians. From the visual acuity and the dimensions of the eyeball you can evaluate the order of magnitude of the dimensions of the receptor cells in the retina, on the hypothesis that two objects become undistinguishable when the light coming from them falls on the same cell. If your vision is poor, perform this experiment with eyeglasses. The same exercise can be performed with a single line of 1 mm width. Are the results consistent? Try to explain why or why not.

13. ASTIGMATISM:

Ideally all refracting surfaces in an optical system should be symmetric about a common axis. In the eye, no surfaces are perfectly spherical, perfectly symmetric, or aligned to a common axis. Some of these `defects' are not noticeable in normal vision. If the eyeball is off-round, or the lens is off-round, the distortion may show up as astigmatism.

Astigmatism test pattern.

(This chart, in printed form, or on a computer screen may not have equal resolution of the lines at all angles. For a proper test of astigmism use a printed chart intended for that purpose.)

Find someone in class who has glasses that correct for astigmatism. (Or obtain a astigmatic lens from the instructor.) Look through it and rotate it as you look.

You may 'construct' an astigmatic lens by combining a weak cylindrical lens with a spherical lens. Chances are good that someone in the class has astigmatism, and therefore has eyeglass lenses that are astigmatic, and may be used for this exercise. An optometrist or a shop that grinds lenses for eyeglasses may have "reject" astigmatic lenses they would happily donate to a physics lab.

We include a standard chart used for diagnosing astigmatism. But you should use a precisely printed version, not subject to the distortians of a digitized picture. Look at the spokes of this pattern. If some seem clearer (more distinct and well resolved) than others, it indicates you have some astigmatism. If you don't, look at the pattern through an astigmatic lens, and experience what a person with astigmatism would see.

If you have astigmatism, experiment with corrective astigmatic lenses to see if you can determine your own corrective prescription.

Since no optical surface in the eye is perfectly spherical, nor even symmetric about a common axis, one would expect that even a normal eye should show some astigmatism and coma in images of off-axis objects. However, since the eye's resolution is so poor off-axis, there may be no simple way to demonstrate it.

14. THE PULFRICH PHENOMENON: (13)

Neutral color grey filters are provided. Dark sunglasses may be used. Cover one eye with the filter while observing a pendulum swinging against a featured background.

The nerve signal from a dim image takes several milliseconds longer to reach brain than from a bright one. Therefore if we darken the retinal image of one eye, signals from that eye are delayed. The delay is large enough that if we observe a moving object (such as a swinging pendulum), that pendulum can seem to be nearer or farther from our eyes, depending on whether it is swinging left-right or right-left across our visual field. As a test of your verbal skill at explanation, write up an explanation of the Pulfrich pendulum phenomenon, based on your observations and your understanding of how 3-D vision works. Can you estimate the time delay?

From your observations, and what you know about pendulums, estimate the time delay of the signal to the brain caused by the dark filter.

A physiologist suggested to me that it's more fun to hold the pendulum by hand as you look at this. And especially, you should look down on the pendulum from above as you hold it. The bob seems to rise and fall, in an unexpected manner. You may then experience the feeling that the string pulls on your hand in phase with the apparent (not actual) motion of the pendulum. Thus your vision is convincing your brain of something that isn't so, and this even prejudices your brain's judgment of what your hand feels. It's spooky! (14)

Use the gray filter over one eye to watch a TV action show. People moving across the screen will appear to be nearer or farther than the background. A few years back there was a proposal to use this for a 3d effect in TV shows, ensuring that the motion of nearby objects was always in the direction to make them appear nearer. This is one of the stupider ideas to come out of Hollywood, for the dramatic effect would be unlikely to be good enough to persuade people to wear glasses with one dark filter. One can use one 'lens' of a pair of sunglasses for these experiments.

Wear the filter over one eye while riding (not driving) in an automobile and look out the side window while the driver drives slowly. Watch as someone else passes your car. It will appear that the passing car is moving slower, or faster, than it actually is. (15)

15. STEREOSCOPIC VISION: (16)

The strongest visual clue to depth and distance of nearby objects (nearer than 50 feet) is the parallax due to the 2.5 inch horizontal spacing of our eyes. This gives our brain two clues to the distance of objects (1) the signals from the muscles that converge the eyes toward a nearby object, and (2) the differences between the two retinal images. (17)

Two kinds of information are important here: (1) A sense of absolute distance of an object, even when seen in featureless surroundings. (2) Relative distance of two objects.

A display may be available that has various objects at different distances in a closed box or room, allowing you to look at them with only one eye. You will probably have difficulty determining the distance and size of the objects. Then when you are allowed to use both eyes, you can make those judgments much better. Even with one eye, you can judge distance and size by moving the eye laterally.

Apparatus: Old-fashioned stereoscope with some view cards. Modern stereoscope with some stereo slides. Aerial photographs and their special viewer. Examples of the Stare-e-o-gram pictures currently popular. Examples from Science of molecular models for parallel viewing. Examples for cross-eyed viewing (Schadewald). Bela Julesz examples. Stereo projector, 3d slides, and polarizing glasses. These will be explained, and some demonstrated. See the material on free viewing 3D in the introduction to the optics section of this manual.

15. HAIDINGER'S BRUSH: (18)

Some people can detect polarization directly. You may try this, but do not be too disappointed if you cannot detect this very subtle effect.

Simulation of the
appearance of Haidinger's
brush for vertically
polarized light.
Size and intensity
exaggerated for clarity.

First, use a polarizing sheet in front of the eye and look at a brightly illuminated white paper. After a minute or two you will see a pattern in the center of the field of vision. The pattern looks like a four-leafed clover. Two opposite `leaves' are bluish, the other two are yellowish or brownish. Some describe it as a `diffuse cross'.

The pattern is formed in the `yellow spot' of the eye, which has dichroic tissue. Rotate the polarizing sheet, and the pattern rotates with it.

Now look through the polarizing sheet at an area of blue sky in a direction at right angles to the sun. Again, rotate the polarizing sheet, and note that the pattern is more distinct at some angles. Remove the polarizer and, if you are lucky, you will see the Hadinger brush in the sky. This is not merely an after-image; it will not `fade away'. The pattern results because the skylight is polarized. Thus your eye is a very weak detector of polarized light!

Consult the Wikipedia for other methods for observing this effect.

16. MACULAR DEFECTS:

The Amsler grid.

With advancing age most people develop macular degeneration, which causes a distortion of image at a localized area of the retina. The Amsler grid, reproduced here, can show this, if it is present. The grid consists of straight lines spaced 1/2 cm apart. Look, with one eye covered, at the dot in the center of the grid, from normal reading distance. Do any of the lines seem to have sections that aren't straight? These defects may be quite small, perhaps only over a 0.5 cm portion of the line (the grid lines are 0.5 cm apart). Now test your other eye. Now look with both eyes. If there were any defect, you might not see it when looking with both eyes, since one eye has learned to compensate for the other. If you see any such distortion, mention it to your eye doctor next time you visit.

You may be able to see the distortion of the amsler grid in the digitized version reproduced here. You should obtain a better quality printed version of the grid from your optometris. You can then check your own vision with this grid at home, any time you wish.

17. STANDARD OPTICAL ILLUSIONS:

A collection of standard optical illusions will be made available in the laboratory for your study. Those of special interest to us are illusions of size, and illusions of shape. These warn us not to uncritically accept the 'evidence of our eyes.'

Also, my Visual Illusions document has illusion examples. My 3D illusions has stereo illusions.

18. DYNAMIC OPTICAL ILLUSIONS:

Many classic optical illusions depend on motion. The study of these is more in the discipline of psychology and physiology than in physics.

Have you ever been watching the closing titles of a movie scrolling steadily upward in a theater or on TV, and then noticed that when you looked at stationary objects, they seemed to be moving downward? This is an example of the Waterfall Effect, first described by R. Adams in 1834. One explanation of this was that the eyes follow the movement of the text in the field of vision, to stabilize the image on the retina. This repeated movement persists. However, this plausible explanation, supported by evidence that periodic motions of the eyes tend to persist, turns out to be wrong. Plateau did the experiment with a rotating Archimedes spiral. The spiral appears to expand or contract when rotating. If one then quickly looks at a picture, or the back of one's hand, the pattern there seems to contract or expand in a most surprising manner. (19)

Recent neurological experiments by Roger B. H. Tootell's group at Massachusetts General hospital have helped explain this. Their subjects looked at expanding concentric rings. When the rings stopped expanding, subjects saw them appear to contract, for up to 10 seconds. During this, the subject's brains were being scanned with MRI (magnetic resonance imaging). While the expanding rings were being seen, neural activity was observed in the V5 area of the visual cortex, one of the `higher' processing level regions of the visual cortex. After the rings stopped expanding, activity in this region increased slightly. The explanation is this: In this region of the cortex there are neurons specifically responsive to particular types of motion. While watching expanding motion, the neurons responsible for seeing contracting motion are inhibited. When the expanding motion ceases, the previously inhibited neurons erupt into firing activity for a short while. (20)

19. COLOR VISION:

There's general agreement that the retina has three types of `cone' cells that have different color sensitivity due to their having red, blue or green absorbing pigments. The figure shows their relative sensitivities. The blue pigment is least absorbing, capturing only about 1% as many quanta as the green and red pigments.

Some people lack one or more of the pigments, and their vision is said to suffer from dichromacy or monochromacy, commonly called `color blindness.' (21) Special color pictures are often used to detect color blindness. These are available either as a set of lantern slides, or in book form. A set is available in laboratory. Try them.

20. CHROMATIC ABERRATION:

Psychophysically determined estimates
of the absorption spectra of three
pigments in the human eye.
From Cornsweet, after Wald, 1964.

Chromatic aberration is fairly strong in the human eye, and it must be taken into account when evaluating the quality of retinal images. Nevertheless, for reasons that are not presently understood, measurements of visual acuity are scarcely affected when chromatic aberration is eliminated (Luria and Schwartz, 1960). Thus, chromatic aberration is mentioned here because it ought to affect visual perception, but present evidence indicates that it does not. (22)

I've not found any simple way to demonstrate the presence of chromatic aberration of the eye without elaborate equipment. (23) Yet chromatic aberration is a useful diagnostic tool. Some optometricians use chromatic aberration as a means to understand whether one is overcorrecting or undercorrecting vision. The patient looks at a double figure on the wall, half in a red field, half in a green field and tells which is in better focus. Try this. (24) Perhaps you can devise some other clever and simple way to demonstrate it.

21. EXPERIMENTS YOU CAN DO AT HOME:

A TV experiment. Turn your TV on. Look at it and hum so loudly that you feel the vibration in the mask of your face. Now run up and down the scale to find the right frequency that causes horizontal grey bars to move vertically up or down the screen. The humming causes the eyes to vibrate and changing the pitch makes a harmonic of the vibration match the raster scan.

Jearl Walker's Flying Circus of Physics has a rich collection of other optical experiments you can do with simple apparatus, or no apparatus. See his chapter 5.


Endnotes:

1. This becomes obvious when you try to see underwater. The refraction at the cornea is much reduced, being now an interface between water (1.33) and cornea (1.376). Your eye's optical power drops from about 58 to only about 20. You underwater vision is then very far-sighted. Now compare underwater vision with a face or eye mask that keeps water away from your cornea. The mask window may distort the view, in a manner that depends on whether its window is flat, or curved.

2. The blind spot was discovered by the 16th Century French physicist Edmé Mariotte (1620-1684). Mariotte also independently discovered the inverse relationship between pressure and volume of a gas (called Boyle's law today). Mariotte, however, clearly understood that this relation requires that the temperature of the gas be held constant, an important fact that Boyle did not realize.

3. MIL-HDBK-141, p. 4-7.

4. Historical note: Bifocals were invented by Benjamin Franklin.

5. This phenomenon depends on spatial coherence, which is one of the important qualities of laser light. Jearl Walker points out that sunlight is sufficiently coherent that the speckle can be observed in light reflected from a flat black sheet of paper in sunlight. Do not use a mirror. The sunlight intensity must be reduced, and the black paper helps ensure that. The low-power laser is actually safer in that you can't have mishaps from careless experimental conditions. Walker's explanation of the speckle pattern suggests that the eyes have nothing on the featureless paper to focus on, so they focus at the most comfortable distance. This argument is obviously inadequate, for your eyes do focus and aim at the distance of the paper sheet, the clue being the edges of the sheet.

6. This section is from Palmer.

7. In some individuals the edge may shift the other way. From Cornsweet, p. 56. "[Spherical aberration] is also used, somewhat imprecisely, to refer to an important form of aberration in the human eye. None of the optically effective surfaces in the eye is perfectly spherical, and the refractive power of the media within the lens of the eye is greater at the center of the lens than at its edges. The particular shapes of the surfaces and the distribution of media are such that, for most eyes, the rays from a point source at infinity do not all meet in a perfect point. In some eyes the outer regions of the cornea and lens have greater refractive power than the middle, while for others, the reverse holds. Further, the extent, and in many subjects even the direction, of this effect changes as the subject focuses on near objects (Ivanoff, 1956). The degradation of the retinal image caused by this property of the eye is called spherical aberration, even though none of the relevant surfaces is actually spherical."

8. Physicist Hermann Helmholtz is said to have remarked that if his instrument maker ever sent him an optical instrument so badly designed as the human eye, he'd send it back to have it rebuilt. He was one of the first physicists to study physiology of sight and hearing. Fortunately our brains have learned to compensate for many of the defects of the eye.

9. These suggestions from Thad Cowan.

10. Cornsweet, p. 24.

11. Cornsweet, p. 356.

12. Suggestion from Silvia Jona.

13. Begbie, p. 170.

14. Thad Cowan, University of Kansas, says, "This is a neat example of visual capture (two contradictory inputs: one from the visual system the other from the kinesthetic system—the eyes have it!"

15. Another suggestion from Thad Cowan. See also Walker.

16. Palmer has an excellent section on this subject, but goes into more detail and the experiment requires considerable time to carry out. The student may wish to consult Palmer and carry out this investigation as an independent project.

17. Good references include Kaufman and Julesz.

18. References: Palmer, p. 255. See also Strong, Ch. 6-6.2 and M. Minnaert, The nature of Light and Color in the Open Air, Dover, 2954, pp. 254-257.

19. Kaufman, p. 402-3.

20. For a fuller description, see Scientific American, July 1995, p. 18-19.

21. Color blindness was first described by chemist John Dalton, who discovered and studied it when he noticed that the colors of chemical reactions he observed didn't agree with what other people saw.

22. This paragraph excerpted from Cornsweet, p. 56.

23. One correspondent suggests that chromatic aberration is the reason why distant signs appear clearer in some colors than others. I am not completely comfortable with this interpretation.

24. Suggestion from Silvia Jona.


Text and line drawings © 1996, 2004 by Donald E. Simanek.