1 THE EYE OBJECTIVES: 1) Know the basic process of image formation by the human eye and how it can be simulated in the laboratory. 2) Measure the far points and the near points of a simulated ideal eye and a myopic eye. 3) Learn to correct near-sightedness and far-sightedness with spectacle lenses. 4) Calculate the power of a spectacle lens required for correction of a near-sighted “eye”. Observe its effect. 5) Observe the phenomenon of astigmatism and learn to correct it with a cylindrical spectacle lens. 6) Determine the depth-of-field of a simulated eye and how it changes as the diameter of the iris diaphragm is varied. 7) Determine your own near point and far point, with (if you wear them) and without spectacles. Calculate the prescriptions based on these measurements. INTRODUCTION Figure 1 shows the optics of a human eye. The eye behaves like a color TV camera with a variable focal lens. Light is first refracted at the front surface of the eye (the cornea), then at the crystalline lens. The iris acts as a variable aperture to control the amount of light that enters the eye. The transmitted light then forms an image on the retina and stimulates the optic nerve, which in turn generates electrical signals to the brain for interpretation. The human eye Figure 1Introductory Physics Experiments v3.7 (Physics 252) 2 The eye changes its focal length by contracting or relaxing the ciliary muscles to change the shape of the crystalline lens. When the ciliary muscles are completely relaxed the crystalline lens is thin and acts as a weak lens (long focal length). The eye can then see the most distant object (the far point). When the ciliary muscles are contracted most and the lens is thickest, it is a strong lens (short focal length), and the eye can see the nearest object (the near point). The ability of the eye to focus at different object distances is called accommodation. For an ideal eye, the far point is infinity (∞) and the near point is about 25 cm. Very few people have such perfect vision. Common imperfections of the eye include: (a) the eyeball is too long, which causes myopia or near sightedness; (b) the eyeball is too short, which causes hyperopia or far-sightedness; (c) the shape of the eyeball is non-spherical, which causes astigmatism. These imperfections can be corrected by using spectacle lenses (eyeglasses) of proper types. In this experiment, you will work with an optical system that simulates a human eye (figure 2). Lens L1 represents the cornea. Lens L2 represents the crystalline lens. You will have two lenses of different focal lengths for L2. One is a weak lens, L2 (far), for viewing distant objects; the other is a stronger lens, L2 (near), for viewing nearby objects. Note that a human eye can adjust its focal length anywhere between those of L2 (far) and L2 (near). The lens equations assume certain sign conventions, which it is useful to gather here: + is used for the focal length of converging lenses, and distances to real images. For light incident from the left, real images form on the right and are inverted. - is used for the focal length of diverging lenses, and distances to virtual images. For light incident from the left, virtual images form on the left and are upright.The Eye (Version 3.7, 1/7/2002) 3 Partner ________________________ Name_______________________ ________________________ Section ______________________ PROCEDURE 1. Normal eye a) Set up the optical system as shown in figure 2. Remove L2 (near). Screw L2 (far) onto the back of the fixed lens L1, which is built into the lens stand. Align L1 and R along the axis of the optical bench. Put the variable aperture and the object O aside for now. Look through the eyepiece behind the retina (screen) at a distant object, such as a building or tree outside the window. Move the retina back and forth along the bench until a sharp image is obtained. Estimate the distance from L1 to this object (far point, or FP). Then tighten all the mounts on the bench and measure the distance from L1 to the retina (length of the “eyeball”). S L L1 2RO O = Object S = Spectacle Lens (if needed) L1 = Cornea (fixed) L2 = Crystalline Lens: either L2 (near) or L2 (far) R = Retina Figure 2 b) Replace L2 (far) by L2 (near) and measure the near point. To do this, place the object on the bench. Look through the eyepiece of the retina and move the object back and forth until a clear image of the object is obtained. Now the distance from L1 to the object is the near point (NP). You will notice that there is a moderate range of object distances for which a clear image can be obtained. This range is called the depth of field. Record the two extreme near points in between which you can obtain a clear image. Then calculate the depth of field. Length of the “eyeball” = ________________ cm FP (estimated) = ________________ m NP(1) = ________________ cm NP(2) = ________________ cm Depth of field = |NP(1) - NP(2)| = ________________ cmIntroductory Physics Experiments v3.7 (Physics 252) 4 c) Place the variable aperture in front of L1. Observe the effect the aperture size has on the depth of field. Small aperture: NP(1) = ________________ cm NP(2) = ________________ cm Depth of field = |NP(1) - NP(2)| = ________________ cm Large aperture: NP(1) = ________________ cm NP(2) = ________________ cm Depth of field = |NP(1) - NP(2)| = ________________ cm Q: What is the effect of aperture on the depth of field, based on your three measurements? 2. Near-sighted Eye a) Increase the length of the “eyeball” by moving the retina (screen) back by 2.0 cm. This is equivalent to making the “eye” near-sighted. For the rest of this section keep the retina at this new position. b) Measure the new near point. [You should still be using L2 (near).] c) Replace L2 (near) by L2 (far), and measure the new far point. Increase in the length of the “eyeball” = 2.0 cm NP = ________________ cm FP = ________________ cm d) Calculate the focal length of the spectacle lens. We want to use it to correct the near-sighted eye, so that the corrected eye (eye plus spectacle lens) will have a normal far point of infinity (∞). To do this, use the thin lens equation 1s+1s'=1f where s is the object distance, s' is the image distance (s'>0 for real image; s'<0 for virtual image), and f is the focal length of the spectacle lens (f>0 for a