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Understanding Lenses and Ciliary Muscles in Physics 102 Lecture 19

This lecture covers the principles of lenses, focusing and the role of ciliary muscles in the eye. Discover how lenses bend light and affect the focal length. Explore the amazing capabilities of the human eye.

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Understanding Lenses and Ciliary Muscles in Physics 102 Lecture 19

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  1. Ciliary Muscles Physics 102: Lecture 19 Lenses and your EYE • Today’s Lecture will cover textbook sections 23.9, 24.1, 3-4, 6 Physics 102: Lecture 19, Slide 1

  2. F Review of LensesPreflight 18.8 Focal point determined by geometry and Snell’s Law: n1 sin(q1) = n2 sin(q2) n1<n2 P.A. Fat in middle = Converging Thin in middle = Diverging Larger n2/n1 = more bending, shorter focal length. n1 = n2 => No Bending, f = infinity Lens in water has _________ focal length! Physics 102: Lecture 19, Slide 2

  3. F Review of LensesPreflight 18.8 Focal point determined by geometry and Snell’s Law: n1 sin(q1) = n2 sin(q2) n1<n2 P.A. Fat in middle = Converging Thin in middle = Diverging Larger n2/n1 = more bending, shorter focal length. n1 = n2 => No Bending, f = infinity Lens in water has larger focal length! Physics 102: Lecture 19, Slide 3

  4. Review: Converging Lens Principal Rays Image Assumptions: • monochromatic light incident on a thin lens. • rays are all “near” the principal axis. F P.A. Object F 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to principal axis. Image is real, inverted and enlarged

  5. Preflight 19.1 A converging lens is used to project a real image onto a screen. A piece of black tape is then placed over the upper half of the lens. How much of the image appears on the screen? Physics 102: Lecture 19, Slide 5

  6. Preflight 19.1 A converging lens is used to project a real image onto a screen. A piece of black tape is then placed over the upper half of the lens. Java Physics 102: Lecture 19, Slide 6

  7. Preflight 19.1 Still see entire image (but dimmer)! Java Physics 102: Lecture 19, Slide 7

  8. Lens Equation do f di F Image P.A. Object F • do = distance object is from lens: • Positive: object __________ lens • Negative: object __________ lens Example • di = distance image is from lens: • Positive: ________ image (behind lens) • Negative: ________ image (in front of lens) di = • f = focal length lens: • Positive: ___________ lens • Negative: ___________ lens m =

  9. Lens Equation do f di F Image P.A. Object F • do = distance object is from lens: • Positive: object in front of lens • Negative: object behind lens Example • di = distance image is from lens: • Positive: real image (behind lens) • Negative: virtual image (in front of lens) • f = focal length lens: • Positive: converging lens • Negative: diverging lens

  10. Ciliary Muscles Amazing Eye • One of first organs to develop. • 100 million Receptors4 million • 200,000 /mm22,500 /mm2 • Sensitive to single photons! • Candle from 12 miles Physics 102: Lecture 19, Slide 10

  11. Ciliary Muscles ACT: Focusing and the Eye Cornea n= 1.38 Lens n = 1.4 Vitreous n = 1.33 Which part of the eye does most of the light bending? 1) Lens 2) Cornea 3) Retina 4) Cones Physics 102: Lecture 19, Slide 11

  12. Ciliary Muscles ACT: Focusing and the Eye Cornea n= 1.38 Lens n = 1.4 Vitreous n = 1.33 Which part of the eye does most of the light bending? 1) Lens 2) Cornea 3) Retina 4) Cones Lens and cornea have similar shape, and index of refraction. Cornea has air/cornea interface 1.38/1, 70% of bending. Lens has Lens/Vitreous interface 1.4/1.33. Lens is important because it can change shape. Laser eye surgery changes Cornea

  13. Example Eye (Relaxed) 25 mm Determine the focal length of your eye when looking at an object far away. Object is far away: Want image at retina: Physics 102: Lecture 19, Slide 13

  14. Object is far away: Want image at retina: Example Eye (Relaxed) 25 mm Determine the focal length of your eye when looking at an object far away. Physics 102: Lecture 19, Slide 14

  15. Example Eye (Tensed) 250 mm 25 mm Determine the focal length of your eye when looking at an object up close (25 cm). Object is up close: Want image at retina: Physics 102: Lecture 19, Slide 15

  16. Object is up close: Want image at retina: Example Eye (Tensed) 250 mm 25 mm Determine the focal length of your eye when looking at an object up close (25 cm). Physics 102: Lecture 19, Slide 16

  17. A person with normal vision (near point at 26 cm) is standing in front of a plane mirror. What is the closest distance to the mirror where the person can stand and still see himself in focus? Preflight 19.3 1) 13 cm 2) 26 cm 3) 52 cm Physics 102: Lecture 19, Slide 17

  18. A person with normal vision (near point at 26 cm) is standing in front of a plane mirror. What is the closest distance to the mirror where the person can stand and still see himself in focus? 26cm 13cm Preflight 19.3 1) 13 cm 2) 26 cm 3) 52 cm Image from mirror becomes object for eye! Physics 102: Lecture 19, Slide 18

  19. Multiple Lenses Image from lens 1 becomes object for lens 2 1 2 Example f1 f2 Complete the Rays!! Physics 102: Lecture 19, Slide 19

  20. Net magnification: mnet = m1 m2 Multiple Lenses: Magnification 1 2 do = 15 cm L = 42 cm di = 8.6 cm f1 f2 f1 = 10 cm f2 = 5 cm Example di = 30 cm do=12 cm Physics 102: Lecture 19, Slide 20

  21. Near Point, Far Point • Eye’s lens changes shape (changes f ) • Object at any do can have image be at retina (di = approx. 25 mm) • Can only change shape so much • “Near Point” • Closest do where image can be at retina • Normally, ~25 cm (if far-sighted then further) • “Far Point” • Furthest do where image can be at retina • Normally, infinity (if near-sighted then closer) Physics 102: Lecture 19, Slide 21

  22. Too far for near-sighted eye to focus do Near-sighted eye can focus on this! dfar Contacts form virtual image at far point – becomes object for eye. If you are nearsighted... (far point is too close) Example flens = Want to have (virtual) image of distant object, do = , at the far point, di = -dfar. Physics 102: Lecture 19, Slide 22

  23. Refractive Power of Lens Diopter = 1/f where f is focal length of lens in meters. Person with far point of 5 meters, would need contacts with focal length –5 meters. Doctor’s prescription reads: 1/(-5m) = –0.20 Diopters Physics 102: Lecture 19, Slide 23

  24. If you are farsighted... Too close for far-sighted eye to focus do dnear Far-sighted eye can focus on this! Contacts form virtual image at near point – becomes object for eye. (near point is too far) Example Want the near point to be at do. When object is at do, lens must create an (virtual) image at -dnear. flens =

  25. If you are farsighted... Too close for far-sighted eye to focus do dnear Far-sighted eye can focus on this! Contacts form virtual image at near point – becomes object for eye. (near point is too far) Example Want the near point to be at do. When object is at do, lens must create an (virtual) image at -dnear.

  26. Preflight 19.4 Two people who wear glasses are camping. One of them is nearsighted and the other is farsighted. Which person’s glasses will be useful in starting a fire with the sun’s rays? Physics 102: Lecture 19, Slide 26

  27. Farsighted person’s glasses are converging – like magnifying glass! Preflight 19.4 Two people who wear glasses are camping. One of them is nearsighted and the other is farsighted. Which person’s glasses will be useful in starting a fire with the sun’s rays? Physics 102: Lecture 19, Slide 27

  28. q q q q Angular SizePreflight 19.6, 19.7 Both are same size, but nearer one looks bigger. • Angular size tells you how large the image is on your retina, and how big it appears to be. • How small of font can you read? HighwireCaramel ApplesRabbits KindergartenHello ArboretumHalloweenAmazing Physics 102: Lecture 19, Slide 28

  29. object h0 q N Unaided Eye How big the object looks with unaided eye. Bring object as close as possible (to near point N) **If q is small and expressed in radians. Physics 102: Lecture 19, Slide 29

  30. magnifying glass virtual image object hi ho do di Compare to unaided eye: : Magnifying Glass Magnifying glass produces virtual image behind object, allowing you to bring object to a closer do: and larger q’ Ratio of the two angles is theangularmagnification M: Physics 102: Lecture 19, Slide 30

  31. magnifying glass virtual image (N = near point distance from eye.) object ho hi do  M lies between and the shorter the focal length, the greater the magnification M. Angular Magnification M=N/do di For max. magnification, need image at N, so set di = -N: M =

  32. magnifying glass virtual image (N = near point distance from eye.) object ho hi do For max. magnification, need image at N: so set di = -N: = di < -N  M lies between and the shorter the focal length, the greater the magnification M. Angular Magnification M=N/do di M = 25/10 + 1 = 3.5

  33. See you next class! • Read Sections 25.1, 3-4 Physics 102: Lecture 19, Slide 33

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