Physics 102: Lecture 19 Lenses and your EYE

1. Ciliary Muscles Physics 102: Lecture 19 Lenses and your EYE

2. Past 2F Inverted Reduced Real Image Object Between F & 2F Inverted Enlarged Real Image Image Object Object Inside F Upright Enlarged Virtual 3 Cases for Converging Lenses 40

3. Only 1 Case for Diverging Lenses Image Example F P.A. Object F Image is always virtual, upright, and reduced. 45

4. 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. Smaller n2/n1 = less bending, longer focal length. n1 = n2 => No Bending, f = infinity Lens in water has larger focal length since n2/n1 is smaller! 5

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. 8

6. Preflight 19.1 Still see entire image (but dimmer)! (37% got correct) “There are still rays from the image bouncing off the lower half of the lens that will project the image. ” 8

7. Lens Equation Same as mirror 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 11

8. Lens Equation do f di F Image P.A. Object F Example • If d0 larger, di is smaller, |m| smaller • If d0 smaller, di is larger, |m| larger 11

9. Multiple Lenses Image from lens 1 becomes object for lens 2 1 2 Example f1 f2 Lens 1 creates a real, inverted and enlarged image of the object. Lens 2 creates a real, inverted and reduced image of the image from lens 1. The combination gives a real, upright, enlarged image of the object. 32

10. do = 15 cm f1 = 10 cm di = 30 cm Multiple Lenses: Magnification 1 2 f1 f2 f2 = 5 cm Example First find image from lens 1. 35

11. di = 8.6 cm f2 = 5 cm do=12 cm Multiple Lenses: Magnification 1 2 do = 15 cm L = 42 cm f1 f2 f1 = 10 cm Example di = 30 cm Now find image from lens 2. Notice that do could be negative for second lens! 38

12. 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 40

13. Ciliary Muscles The Eye • One of first organs to develop. • ~100 million Receptors • ~200,000 /mm2 • Sensitive to single photon! • Candle from 12 miles 15

14. 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 17

15. 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. 21

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). 25

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? 26cm 13cm Preflight 19.3 51% 39% 10% 1) 13 cm 2) 26 cm 3) 52 cm Image from mirror becomes object for eye! 28

18. Near Point, Far Point • Eye’s lens changes shape (changes f ) • Object at any do should 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)

19. 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. flens = - dfar If you are nearsighted... (far point is too close) Example Want to have (virtual) image of distant object, do = , at the far point, di = -dfar. 42

20. Refractive Power of Lens Diopter = 1/f where f is focal length of lens in meters. • Example: • My prescription reads -6.5 diopters • flens = -1/6.5 = -0.154 m = -15.4 cm (a diverging lens) • dfar = 15.4 cm (!) flens = - dfar 43

21. 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. 45

22. Farsightedness • Near point dnear > 25 cm • To correct, produce virtual image of object at d0 = 25 cm to the near point (di = dnear) • Example: • My near prescription reads +2.5 diopters • flens = +1/2.5 = 0.4 m = 40 cm • therefore dnear = 67 cm (with my far correction)

23. Farsighted person’s glasses are converging – like magnifying glass! ACT/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? • nearsighted • farsighted Does it help if you have a high prescription?

24. See you next Monday