1Physics 211Optical Instruments
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 byforming an image that stimulates nerveendings, creating the sensation of sight.The eye consists of anaperture and lens system at the front,and a light-sensitive surface at the back.Light enters the eye through the aperture-lens system, and is focused on theback wall.The lens system consists of two lenses:the corneal lens on the front surface ofthe eye, and the crystalline lens inside
the eye. The space between the lenses isfilled with a transparent fluid called theaqueous humor. Also between thelenses is the iris, an opaque, coloredmembrane. At the center of the iris isthe pupil, a muscle-controlled, variable-diameter hole, or aperture, which
controls the amount of light that entersthe eye. The interior of the eye behind the crystalline lens is filled with a colorless, transparentmaterial called the vitreous humor.On the back wall of the eye is the retina, a membrane containing light-sensitive nervecells known as rods and cones. Rods are very sensitive to low light levels, but provideus only with low-resolution black-and-white vision. Cones allow us to see incolor 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 acutevision. 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 nolight-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 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 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 pupilaperture 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 representsthe blind spot. The retina screen can be placed in three different positions(labeled NORMAL, NEAR, and FAR) to simulate a normal, near-sighted, or farsightedeye.
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 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 lightsource 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 rimof the eye model, as pictured below. (The front of the rim is a convenient place tomeasure to and marks the center of the eye model’s two-lens system.) Record thisdistance, which is the near point of the eye model when equipped with the+62 mm lens. Measure and record the near pointfor 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 eye-source 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 near-point 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?
6. Position the eye model (with pupil removed) so that it is looking towards adistant object. Is the image on the retina in focus? Replace the lens in the SEPTUMslot with one that makes a clear image of the distant object; this is the farvisionlens. 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 increaseor 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.) Theserefractive errorsof coursecan 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 lensyou 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 distanceso 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.
Experiment 4: Astigmatism
In a normal eye, the lens surfaces are spherical and rotationally symmetrical; but aneye with astigmatism has lens surfaces that are not rotationally symmetrical. Thismakes the eye able to focus sharply only on lines of certain orientations, and all otherlines look blurred. Astigmatism can be corrected with a cylindrical eyeglass lensthat is oriented to cancel out the defect in the eye. Each cylindrical lens included with the eye model has its cylindrical axis marked bytwo 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.
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 anear 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 lensesforms an upright, real image at infinity.