The Human Eye & Optical Instruments
(adapted from the Pasco manual for the Model Human Eye 8/2008)
In this part of the optics lab, you will learn about the anatomy and optics of the human
eye and do experiments to understand how our eyes form images, and how eyeglasses
correct refractive errors and astigmatism. In the final part, you will investigate the optics
of microscopes and telescopes. You should read all of the background material, but you
can choose to do only the eye experiments or only the optical instrument experiments in
lab (if you have time you can do both.)
Anatomy of the Eye
The human eye achieves vision by forming an image that stimulates nerve endings,
creating the sensation of sight. The eye consists of an aperture and lens system at the
front, and a light-sensitive surface at the back. Light enters the eye through the aperturelens system, and is focused on the back wall. The lens system consists of two lenses: the
corneal lens on the front surface of the eye, and the crystalline lens inside
the eye. The space between the lenses is filled with a transparent fluid called the aqueous
humor. Also between the lenses is the iris, an opaque, colored membrane. At the center
of the iris is the pupil, a muscle-controlled, variable-diameter hole, or aperture, which
controls the amount of light that enters the eye. The interior of the eye behind the
crystalline lens is filled with
a colorless, transparent
material called the vitreous
humor. On the back wall of
the eye is the retina, a
membrane containing lightsensitive nerve cells known
as rods and cones. Rods are
very sensitive to low light
levels, but provide us only
with low-resolution blackand-white vision. Cones
allow us to see in color at
higher resolution, but they
require higher light levels.
The fovea, a small area near
the center of the retina,
contains only cones and is responsible for the most acute vision. Surrounding the fovea is
the sensitive region called the macula, which is responsible for central vision. Signals
from the rods and cones are carried by nerve fibers to the optic nerve, which leads to the
brain. The optic nerve connects to the back of the eye; there are no light-sensitive cells at
the point where it attaches, resulting in a blind spot.
Cameras share the same optical design as the human eye. Cameras of course have glass
or quartz lenses that move mechanically back and forth rather than being fixed in place
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like the crystalline lens and cornea, and they sense light with electronic sensors or film
rather than a retina, but the optical design issues you learn here will apply to cameras.
The Model Eye Apparatus
The PASCO Human Eye Model consists of a sealed plastic tank shaped roughly like a
horizontal cross section of an eyeball. A permanently mounted, plano-convex, glass lens
on the front of the eye model acts as the cornea. The tank is filled with water, which
models the aqueous and vitreous humors. The crystalline lens of the eye is modeled by a
changeable lens behind the cornea. A movable screen at the back of the model represents
the retina. An optics caliper is provided for measuring images on the retina screen.
The lenses of the eye model are equipped with handles, which allow them to be easily
inserted into the water. The handles of the plastic lenses are marked with their focal
lengths in air. Two of the lenses are cylindrical lenses for causing and correcting
astigmatism in the model; these can be identified by notches on their edges that mark the
cylindrical axes.
WARNING: DO NOT wipe or rub
the lenses with a cloth or tissues to
dry or clean them. They are plastic
and easily scratched. We will
provide blow-off guns you can use to
dry them off.
The crystalline lens, which is
supported in the slot labeled SEPTUM,
can be replaced with different lenses to
accommodate, or focus, the eye model
at different distances. (The label refers
to the septum, or partition, formed by
the lens and other tissues, that
separates the aqueous and vitreous
humors.) Two other slots behind the
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cornea, labeled A and B, can hold additional lenses to simulate changing the power of the
crystalline lens. A cylindrical lens can be placed in slot A or B to give the eye
astigmatism. The pupil aperture can also be placed into slot A or B to demonstrate the
effect of a round or “cat-shaped” pupil. Two slots in front of the cornea, labeled 1 and 2,
can hold simulated eyeglasses lenses to correct for near-sightedness, far-sightedness, and
astigmatism.
A circle marked on the retina screen represents the fovea, and a hole in the screen
represents the blind spot. The retina screen can be placed in three different positions
(labeled NORMAL, NEAR, and FAR) to simulate a normal, near-sighted, or farsighted
eye.
Optics of the Eye
The corneal lens and crystalline lens together act like a single, convergent lens. Light
entering the eye from an object passes through this lens system and forms an inverted,
real image on the retina. The eye focuses on objects at varying distances by
accommodation, or the use of muscles to change the curvature, and thus the focal length,
of the crystalline lens. In its most relaxed state, the crystalline lens has a long focal
length, and the eye can focus the image of a distant object on the retina. The farthest
distance at which the eye can accommodate is called the far point for distinct vision. For
a normal eye, the far
point is infinity.
When muscles in the
eye contract and
squeeze the lens, the
center of the lens
bulges, causing the
focal length to
shorten, and allowing
the eye to focus on
closer objects. The nearest distance at which they eye can accommodate is called the
near point for distinct vision. The near point of a normal eye is about 25 cm.
Experiment 1: Image formation
1. Put the retina screen in the
NORMAL slot and the +120 mm
lens in the SEPTUM slot.
2. Fill the model with water.
This simulates the effect of the
aqueous and vitreous humors that
actually fill the eyeball.
3. Aim the eye at a bright, distant
object such as a window or lamp
across the room. An image is
formed on the retina screen.
Observe and record the
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orientation of the image relative to the object (up/down, left-right). Why are you not
aware of any reversals of the retinal image compared to the real-life object?
Experiment 2: Focusing at different distances:
Accommodation
In the process of accommodation, muscles in the eye change the shape of the crystalline
lens to change its focal length. Accommodation in the eye model is simulated by
changing the lens or lenses that represent the crystalline lens.
1. Place the eye model about 35 cm from the light source and object. Place the +62 mm
lens in the SEPTUM slot.
2. Is the image in focus now? Move the eye model as close as possible to the light source
while keeping the image in focus. Describe the image on the retina screen as you move
the eye model.
3. Measure the object distance, o, from the screen of the light source to the top rim of the
eye model, as pictured below. (The front of the rim is a convenient place to measure to
and marks the center of the eye model’s two-lens system.) Record this distance, which is
the near point of the eye model when equipped with the +62 mm lens. Measure and
record the near point for your eyes and those of your lab partner by finding the shortest
distances at which you can focus. (Keep your glasses on if you wear them. Note that
although we’ve given a typical value, your value may be much smaller or larger thant his
value!)
4. Increase the ability of the eye model to focus on a close object by adding the +400 mm
lens to slot B. This combination models a different focal length for the crystalline lens,
due either to accommodation (or wearing reading glasses!) How close can the eye focus
now?
5. Remove both lenses and place the +62 mm lens in the SEPTUM slot. Adjust the eyesource distance to the “near point” distance for this lens (which you found in step 3) so
that the image is in focus. While looking at the image, place the round pupil in slot A.
What changes occur in the brightness and clarity of the image? Move the light source
closer to and farther from the eye model. Is the image still in focus? Remove the pupil
and observe the change in clarity of the image. Both with and without the pupil, how
much can you change the eye-source distance and still have a sharp image?
Note that this effect is not a change in resolution similar to what we discuss later. It’s
simply a way to increase the depth of focus (the range of distances over which images
stay approximately in focus). For a pinhole camera, images are in sharp focus for any
distance, but only a tiny amount of light is transmitted. We have a pinhole camera
available in the lab; you should try this out and understand how it forms images. Ask
your instructor for help if necessary. For a lens of nonzero diameter, the focal plane has a
limited depth. Increasing the aperture allows more light in, but decreases the depth of
focus. Similar tradeoffs are important in photography.
Try on the pinhole glasses (taking off any glasses you ordinarily use) and find your nearpoint with the pinhole glasses on—it should surprise you! Record its value and explain
qualitatively why it has this value. What could you do to make it even smaller?
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6. Position the eye model (with pupil removed) so that it is looking towards a distant
object. Is the image on the retina in focus? Replace the lens in the SEPTUM slot with one
that makes a clear image of the distant object; this is the far vision lens. Record the focal
length marked on the handle of the lens.
7. In a real human eye, accommodation is accomplished by muscles that change the
curvature of the crystalline lens. When an eye changes accommodation from a distant
object to a near object, does the curvature of the crystalline lens increase or decrease?
Relate to your results above. Why does this explain why the eye’s range of
accommodation might decrease with age?
Experiment 3: Refractive errors: near-sightedness and
far-sightedness
A person affected by myopia (near-sightedness) has a longer-than-normal eye ball,
making the retina too far away from the lenses. This causes the image of a distant object
to be formed in front of the retina. By contrast, a person affected by far-sightedness
(hyperopia) has a shorter-than-normal eye ball, making the retina too close to the lens
system. This causes images of near objects to be formed behind the retina. (Aging can
cause a decline in accommodation that results in similar optical effects, a condition called
presbyopia.) These refractive errors of course can be compensated for with eyeglasses
or laser surgery to change the curvature of the cornea. We will explore only the first
condition here.
1. Set the eye model to normal, far vision (put the far lens you found in Experiment 1,
step 7 in the SEPTUM slot, remove other lenses, and put the retina screen in the
NORMAL position). Turn the eye model to look at the distant object. Make sure the
image is in focus. Now put the retina screen in the NEAR position. Describe the image.
This is what a near-sighted person sees when trying to look at a far-away object. The
lens in the SEPTUM slot represents the crystalline lens in its most relaxed, flattest state,
with its longest-possible focal length. Can an eye compensate for myopia by
accommodation? Explain.
2. Decrease the pupil size by placing the round pupil in slot A. What happens to the
clarity of the image? Remove the pupil. This underlies the operation of the pinhole
glasses concept. If you or your partner is near-sighted, try on the pinhole glasses in place
of your own glasses and look at distant objects.
3. You will now correct the myopia by putting an “eyeglass” lens on the model. Find a
lens that brings the image into focus when you place it in front of the eye in slot 1.
Record the focal length of this lens. Does rotating the eyeglasses lens in the slot affect
the image? Why or why not?
4. Set the eye model to near vision (leave the corrective “eyeglass” lens in place, remove
the far vision lens, put the +62 mm near vision lens in the SEPTUM slot, and leave the
retina screen in the NEAR position). With the eye model looking at the nearby light
source, adjust the eye-source distance so that the image is in focus. How does this
compare to the near-point distance you found in Experiment 1? Why?
5. Describe an experiment similar to those above that would probe far-sightedness.
Draw a diagram indicating what your experiment looks like. Perform your experiment
and record which “eyeglass” lens corrects the “far-sighted” eye model.
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Experiment 4: Astigmatism
In a normal eye, the lens surfaces are spherical and rotationally symmetrical; but an eye
with astigmatism has lens surfaces that are not rotationally symmetrical. This makes the
eye able to focus sharply only on lines of certain orientations, and all other lines look
blurred. Astigmatism can be corrected with a cylindrical eyeglass lens that is oriented to
cancel out the defect in the eye. Each cylindrical lens included with the eye model has its
cylindrical axis marked by two notches in the edge.
1. Now look at the astigmatism chart. All of the lines are printed the same thickness and
brightness, but a person with astigmatism sees some lines as darker than others. Cover
one eye and look at the chart both with and without your glasses, if you wear them. Do
some of the lines look darker than others? If they do, rotate the figure 90° to convince
yourself that the lines are actually the same and it is only your eye that causes the effect.
Try rotating your glasses in front of your face while looking at the chart through one of
the lenses. Describe what you see.
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2. Set the eye model to normal, near vision (put the +62 mm lens in the SEPTUM slot,
remove other lenses, and put the retina screen in the NORMAL position). With the eye
model looking at the nearby light source, adjust the eye-source distance so that the image
is in focus.
3. Place the -128 mm cylindrical lens in slot A. The side of the lens handle marked with
the focal length should be towards the light source. Describe the image formed by the eye
with astigmatism.
4. Rotate the cylindrical lens. What happens to the image? This shows that astigmatism
can have different directions depending on how the defect in the eye’s lens system is
oriented.
5. Eyeglasses can be outfitted with compensating cylindrical lenses to correct
astigmatism. Now place the other astigmatic lens in the eyeglass holder slot and move it
until the image is again focused. What manipulation did you have to do to bring the
image into focus again? Describe how you could find out experimentally if a pair of eye
glasses have astigmatic corrections.
Optical Instruments and the Human Eye
Optical instruments enhance vision by forming an image that is a different size or at a
different position from the object:
A microscope is a combination of two or more lenses that forms a distant image of a near
object. The lens nearest the object observed is called the objective lens, and its aperture
determines the light-collection angle and hence the system’s spatial resolution. In the
example illustrated below, a system of two converging lenses forms an upright, real
image at infinity.
A telescope forms a larger image of a distant object. In the example of a simple
refractor telescope illustrated below, a system of two converging lenses forms an
inverted, real image. Note that the image is not closer to the eye than the object; this
telescope forms a distant image which can be viewed by the eye in its relaxed state, when
it is focused at infinity. Because its objective lens, or first lens, usually has a larger area
than the pupil of the eye, a telescope gathers more light than the unaided eye, and thus
can allow the eye to see objects that would normally be too dim to detect.
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Refractor telescopes have the advantage that they form upright images, rather than
inverted images which appear upside-down to us. They are still used for many terrestrial
applications, such as piracy. However, all modern optical research telescopes use mirrors
to provide a much larger diameter aperture for superior light-collecting and for spatial
resolution. (You will learn more details about the latter issue in the Physical Optics Lab.)
One popular design is the Newtonian reflector, which uses a curved (spherical or, ideally,
parabolic) primary mirror to collect light, and focuses that light onto an eyepiece or
camera using a flat secondary mirror at an angle to the primary. One disadvantage of this
design is that the larger aperture the mirror, the longer and heavily the tube required to
mount it.
http://www.telescope-optics.net/reflecting.htm
By contrast, a Schmidt-Cassegrain telescope uses two mirrors: a large primary and a
smaller secondary, both of which are curved. The primary mirror has an aperture in its
center that allows the light to be focused by the secondary onto the eyepiece or a camera.
Note that this design folds the light pathway into a more compact distance even for a
large aperture primary mirror, so the tubes can be shorter than for a Newtonian reflector.
Our large Observatory dome telescopes have this design.
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http://www.geologynet.com/astronomy/telescopes2.htm
Telescopes are also classified by their mounts. Either refractors or reflectors can use
equatorial mounts equipped with angular adjustments that allow tracking of objects in
the sky. This is because equatorial mounts allow the telescope’s optical axis to be
pointed at the North Star, and a second angular adjustment allows celestial objects to be
tracked about the Earth’s axis of rotation so objects in the sky appear at a constant
location in the telescope’s field of view. All research telescopes on Earth have this
design. By contrast, Dobsonian mounts are only used for reflectors. In a Dobsonian
(named for its hippie monk inventor), a Newtonian reflector tube is mounted on an
“altazimuth” base with two angular adjustments: pivoting about a horizontal axis and
rotation about the vertical axis. Because Dobsonians can be built to pivot smoothly and
support a very large mirror inexpensively, they are popular with amateur astronomers.
The bases are low profile and pivot and point easily by hand, although they do not track
the motion of celestial objects. Dobsonians provide a way to stably mount and move
about a very large diameter mirror, since the mirror is mounted stably near the base. For
this reason they are popular with amateur astronomers.
Experiments with Optical Instruments (Try to do at least
one if you have time!)
The resolution limit for microscopes and telescopes is expressed in terms of the Rayleigh
resolution limit, which you’ll learn about in the Physical Optics lab. Basically, it
corresponds to the limit of how fine a spatial feature you can resolve given limits
imposed by diffraction due to the wave-like nature of light. The easiest way to
understand this is to note that even a perfect mathematical point will emit light that’s
focused to a blurry spot by a lens or mirror because of interference and diffraction effects.
If two near-by objects are imaged, then the angle,  in terms of the distance, d, between
two nearby objects and the distance L from the observing optics is   d/L, for small
angles. The smallest resolvable feature is then given by the Rayleigh resolution limit:
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
sin   1.22 D .1 For a telescope, D is the diameter of the objective lens (the one
closest to the object) or primary mirror. You can relate the resolution limit by noting the
distance to a remote object and the smallest feature resolvable: for small angles,  ~
(feature size)/(distance). For the microscope, there is an additional complication, since
resolution is expressed in terms of NA or numerical aperture (see Wikipedia image at
left).
NA  n sin   nD
2f
where n is the index of refraction of the medium between
the lens and the object, and D and f are the objective lens’s
diameter and focal length. (The index of refraction appears
because microscopy sometimes is done using an
intervening layer of high index oil between the sample and
objective, so that refraction allows the objective to capture
a wider range of rays from the object. Telescopes always
operate in air or vacuum, so the index of refraction is
always 1.00 in these cases and can be ignored.) Each microscope objective is marked
both with its magnification and its NA. This gives the effective size resolution limit of
the smallest feature resolvable by a light microscope as 1.22 NA , where the wavelength
is a typical value for visible light (somewhere between 400 and 700 nm.)
Experiment 5: Microscopes
Using our advanced lab low resolution stereomicroscope and the higher resolution
compound microscope, observe their optical components and note how they correspond
to the schematic above. Use the calibration slides provided to quickly observe the effect
of changing resolution when you change the microscope objective power and switch
between the two microscopes. Record how the change in objective relates to light
collection (did you have to increase or decrease the illumination intensity for a fixed
intensity on the screen?), field of view (how large a region of the object gets mapped onto
the entire image) and resolution. Record your resolution limit theoretically and
experimentally for each microscope and objective lens setting, using the calibrated slides
provided. Describe and sketch what the features look like once you approach and exceed
the resolution limit, and explain why.
Comment on whether you saw any of the optical imperfections described on the next
page, and if so, which configuration gave you that effect or did not.
Experiment 6: Telescopes
Using the kit provided, build a refractor telescope, noting how its design maps onto the
schematic above. Also, look at the Newtonian reflector (tube only, no mount) provided.
If you have time, you can disassemble and reassemble it if you wish (be VERY sure it’s
1
Note: actually, the angle (and hence the location) of an individual small object can be measured to higher
resolution than this, because you can always locate the maximum of a diffraction spot to much higher
resolution (i.e., within smaller error bars) than its width due to the resolution limit. Measurements of this
sort at important in modern biology and nanotechnology.
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the one you can take apart), similarly observing its optical design. (A four-vaned frame
called a spider holds the flat secondary mirror in place. Be sure you hold this in position
the entire time until you have all four screws tightened before you let go, or else it will
fall on the primary mirror!) Now use the already-assembled Dobsonian Newtonian
reflector and refractor telescopes to observe the world outside. You can use the windows
in our lab or the Math Lounge. Comment on the smallest size object you can resolve.
Comment on whether you saw any of the optical imperfections described on the next
page, and if so, which configuration gave you that effect or did not. Explain how you
would be able to observe each effect with an experiment. Based on the aperture size of
your telescopes, what would you expect the fundamental resolution limit to be?
Even the Hubble Space telescope was famously fitted with corrective lens to fix its initial
optical imperfections! (Below, images before and after the corrective lens were fitted.
Ugh, who screwed up the optics on the expensive space telescope?)
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http://www.funsci.com/fun3_en/tele/tele.htm



Achromat lenses compensate for chromatic aberrations by using two lenses, one
converging, one diverging, made from different index materials. As a result, the
two lenses give opposite, compensating chromatic aberrations that can be
designed to cancel out.
Using a spherical rather than a parabolic mirror can lead to spherical aberratoins,
although it’s much easier to grind a spherical mirror.
As you’ve seen above, cylindrical lenses can be used to correct for astigmatism.
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Equipment List
1. Human eye model with its optical rail mound
2. Pasco optical rail and light source
3. Small desk lamp for illumination
4. Pinhole camera and pinhole glasses
5. Model of eye anatomy
6. Newtonian reflector (Orion Starblast)
7. Refractor kits from Edmund Scientific
8. Microscopes from H106 (advanced lab)
9. Microscope resolution target (Edmund Optics)