The Eye. Objectives: Introduction. PHY 192 The Eye 1

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1 PHY 92 The Eye The Eye Objectives: Describe the basic process of image formatio by the huma eye ad how it ca be simulated i the laboratory. Kow what measuremets are ecessary to quatitatively diagose ear-sightedess or far-sightedess. Locate the far poits ad ear poits of simulated ideal ad myopic eyeballs. Describe how spectacle leses ca correct far-sightedess or ear-sightedess. Calculate the power ad type of spectacle les required to correct a give simulated ear-sighted eye. Observe its effect. Observe the effects of astigmatism ad its correctio with a cylidrical spectacle les. Determie the depth-of-field of the simulated eyeball ad how it depeds o the diameter of a iris diaphragm ear the leses. Determie your ow ear poit ad far poit with spectacles (if you wear them) ad without spectacles. Calculate your required ad actual prescriptios based o these measuremets. Itroductio Figure shows the optics of the huma eye. It behaves like a color TV camera with a variable focus les. The eye is early spherical, so that it may be rotated easily i it socket. It is focused (accommodated) at differet object distaces by cotractio of the ciliary muscles which chages the radius of curvature of the crystallie les ad thereby chages its focal legth. The iris acts as a variable aperture to cotrol the amout of light that reaches the retia. The light which forms a image o the retia stimulates electrical sigals which travel alog the optic erve to the brai for iterpretatio of the image. Fig. : The huma eye

2 PHY 92 The Eye 2 Optically, most of the refractio of light takes place at the frot surface of the eye (the corea) ad the remaider takes place at the crystallie les. The ciliary muscles ca chage the shape of the crystallie les to focus the eye from its Far Poit (the most distat object which ca be see clearly whe the ciliary muscles are relaxed) to its Near Poit (the earest object which ca be clearly see whe the ciliary muscles are cotracted as much as possible). As metioed above, the process of focusig o earby objects is called accommodatio. For a idealized, so-called "ormal" eye, the Far Poit (FP) is ifiity ad the Near Poit (NP) is about 25 cm. Very few persos have such "ormal" eyes. Simple defects of the eye iclude: havig too log a eyeball, resultig i myopia or ear-sightedess, havig too short a eyeball, called hyperopia leadig to far-sightedess, havig a o-spherical surface, usually the corea, givig rise to astigmatism. Correctio ca be made for each of these defects by usig a spectacle les (eyeglasses) of the proper type ad appropriate focal legth placed i frot of, ad very close to, the eye. Iadequate accommodatio (ability to focus the eye for various distaces) ca be corrected by usig bifocal or trifocal leses, which have segmets of differet focal legths, to provide two or three sharp viewig distaces through the separate parts of the les. I this experimet you will work with a optical system which simulates that of the huma eye, but which is larger i size ad less messy to work with, as we will ot use fluids. Figure 2 shows the optical system that we shall use. Les L represets the refractio which takes place at the frot surface (corea) of the eye ad les L 2 represets the crystallie les. You will have two leses of differet focal legths to isert for L 2, oe L 2 (far) for its behavior whe viewig distat objects, ad oe L 2 (ear) for its behavior whe viewig earby objects. Remember that the crystallie les of a actual eye ca be accommodated for ay value of focal legth betwee those of L 2 (far) ad L 2 (ear). O S L L 2 R O = Object S = Spectacle Les L = Corea L 2 = Crystallie Les R = Retia Optical Bech Fig. 2: Optical Equivalet of the Eye

3 PHY 92 The Eye 3 Procedure Note: All distaces are measured from the corea i.e. L. The "Normal Eye" a) Set up the optical system as show i Figure 2 with L 2 (far) placed close to L, ad without the object o the optical bech. Adjust the positio of the retia so that a sharp image is obtaied for the most distat objects you ca use. Look out the widow at a distat buildig or tree or light. Record your estimate of the distace from L to this object. Tighte all the mouts o the bech ad measure the "legth" of the eyeball from L to R. b) Substitute les L 2 (ear) for L 2 (far) ad measure the actual ear poit, NP, of the system usig the object o the bech. Repeat this measuremet several times ad record the ear poit values from L. NOTE: There will be a moderate rage of object distaces for which a clear image is obtaied. This rage is called the depth of field of the optical system. c) From the rage of values for NP, calculate the mea NP = NP i ad i= the stadard deviatio ucertaity i the mea σ m = ( ) ( NPi NP ) i= 2. Here, is the umber of your measuremets of the NP. These will provide the best estimate of the true value for NP ad its ucertaity. Your istructor ca show you how to do this with Kaleidagraph. A discussio of these expressios ca be foud i Chapter four of Taylor. The "Nearsighted Eye" a) Icrease the legth of the "eyeball" by 2.0 cm, by movig the retia (viewig scree) back. b) Measure the actual ear poit alog the optical bech (from L ) several times. Determie the best value ad its ucertaity. c) Replace L 2 (ear) by L 2 (far) ad measure the actual far poit alog the optical bech several times. Determie the best value for the far poit ad its ucertaity. d) Calculate the proper focal legth of a spectacle les so that the system, icludig the spectacle les will have a ormal far poit at ifiity.

4 PHY 92 The Eye 4 To do this, use the thi les equatio f = s + s', where s is the object distace, s' the image distace, ad f the focal legth of the spectacle les. I this applicatio, s is the desired object distace, viz., ifiity, s' = -FP as obtaied i 2(c). Covert the focal legth obtaied i this maer ito the power of the les as specified by optometrists, usig the equatio: P = 00/f(cm) diopters to specify the required spectacle les. (Positive power values deote covergig leses ad egative power values divergig leses.) e) Choose from the available leses the oe closest i power to the value you obtaied i (d) ad mout it very close to ad i frot of L. f) Measure ad record the far poit ad the ear poit of your system, icludig the spectacle les. g) Compare your measuremets of ear ad far poits with your expectatios. The "Astigmatic Eye" a) Place the weak cylidrical les L 3 i frot of L ad L 2 (ear), ad examie the appearace of the image of the object cosistig of several radial lies, as the object distace is varied, ad the as the eye legth is varied. (This is ot the way the eye works but the effect o the image is the same.) The effect you are seeig is astigmatism. Sketch its appearace for several settigs to show the rage of possible appearaces. b) Mout the "matchig" cylidrical les L 4 i frot of L 3 ad rotate it i its mout util the astigmatism is corrected. Measuremet of ow NP ad FP. a) without spectacles (glasses) b) with spectacles, if you wear them Depth of Field Place the variable aperture ear L ad observe the effect of its diameter o the "depth of field" (rage of object distaces producig a "sharp" image) ear the ear-poit of the system used i "Normal Eye" (b). (Squitig ca produce a somewhat similar effect.)

5 PHY 92 The Eye 5 Report Iclusios Your report should iclude:. a) sketch of optical system b) value of far poit of ormal system c) best value of ear poit of ormal system ad its ucertaity 2. a) best value of ear poit of myopic system ad its ucertaity b) best value of far poit of myopic system ad its ucertaity c) calculatio of f ad P for spectacle les d) values of far poit ad ear poit of system plus spectacle les e) compariso with hoped-for result 3. a) sketches ad descriptio of "visual" effects of astigmatism b) descriptio of maer ad success of correctio for astigmatism 4. Estimates of your ow ear poits ad far poits 5. Descriptio of effects of variable aperture o image obtaied