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Vision: Focusing W. Rose See Martini & Ober (VA&P), chapter 15. See Marieb & Hoehn (9th ed.), chapter 15. Useful source of information: http://hyperphysics.phy-astr.gsu.edu/hbase/vision/visioncon.html Department of Kinesiology and Applied Physiology Object distance o Image distance i Figures from Visual Anatomy and Physiology, © 2011. Image distance* (i) is determined by lens shape (curvature, C) and distance to object being viewed (o). * VA&P calls the image distance "focal distance". Department of Kinesiology and Applied Physiology i 1 1 C o Equation for a lens made of glass, in air. Object distance o Image distance i Figures from Visual Anatomy and Physiology, © 2011. i 1 1 C o When an object is far away, the object distance o is large. When o gets large, i gets small (if curvature is constant). When o=infinity, i=1/3C. Department of Kinesiology and Applied Physiology Object distance o Image distance i When lens curvature C increases (rounder lens), image distance i gets smaller (if o is constant). i 1 1 C o Department of Kinesiology and Applied Physiology Summary 1. When object distance o gets smaller, image distance i gets larger (if curvature is constant). 2. When curvature C increases, i gets smaller (if o is constant). 3. Therefore, if C increases while o decreases (lens gets rounder as object gets closer), it is possible to keep i constant. In other words, the image will stay in focus at a constant distance from the lens. This is what we want for vision, since the distance from lens to retina is constant. i 1 1 C o Department of Kinesiology and Applied Physiology Background page showing the derivation of the equation for i. Thin lens equation 1 1 1 o i f 1 1 1 i f o 1 i 1 1 f o Top equation above is offered without proof. For a glass lens in air: 1 C f where C = lens curvature: a flat lens has low curvature, a round lens has high curvature. C=1/R, R=radius of curvature, presumed same on front & back of lens. Image distance i i 1 1 C o Image distance (i, distance to focal point) depends on object distance (o) and lens shape (curvature C). Equation above follows from the equations in the previous boxes. Department of Kinesiology and Applied Physiology More background: glass lens in air versus human lens in ocular humors. Thin lens immersed in a medium with index n0: n n 1 lens o 1 1 no R R f 1 2 Glass in air, double convex R1=1/C, R2= -1/C: Human lens, aqueous & vitreous humor: 1 1.512C C f 1 1 1.411.34 2C 0.1C f 1.34 i Top equation above is offered without proof. 1 C 1 o Image distance i C=1/R, R=radius of curvature, presumed same on front & back of lens. i 1 0.1C 1 o Lower equations follow from top equation and from 1/f=1/i+1/o. Department of Kinesiology and Applied Physiology How is the non-uniform refractiveindex of the lens handled in the model? To answer , compare results on slide to calculations of powers: P = (n2-n1) / R From aqueous humor into lens, using central n2: n1=1.336, n2=1.406, R=.008672 P=0.070/.008672=8.07m-1 This calculated power matches the result on the diagram. Evidently the model uses the central lens index for calculations. Eye model by Carl Rod Nave. Retreived 2012-05-09. http://hyperphysics.phy-astr.gsu.edu/hbase/vision/eyescal.html Model check: Sum of powers = 63.7 m-1, which corresponds to focal length 15.7 mm, which equals model distance from back of lens to retina (estimated by measurements on diagram above and by subtracting sum of distances listed from 24 mm). Note: Real lens has greater index of refraction (n) at center than at periphery. A check shows that the model uses the central n to compute focusing power. Department of Kinesiology and Applied Physiology