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

3. Physics 102: Lecture 19, Slide 2 Review of Lenses Preflight 18.8 P.A. F Focal point determined by geometry and Snell’s Law: n 1 sin(   ) = n 2 sin(   ) Fat in middle = Converging Thin in middle = Diverging Larger n 2 /n 1 = more bending, shorter focal length. n 1 = n 2 => No Bending, f = infinity Lens in water has _________ focal length! n 1 <n 2

4. Physics 102: Lecture 19, Slide 3 Review of Lenses Preflight 18.8 P.A. F Focal point determined by geometry and Snell’s Law: n 1 sin(   ) = n 2 sin(   ) Fat in middle = Converging Thin in middle = Diverging Larger n 2 /n 1 = more bending, shorter focal length. n 1 = n 2 => No Bending, f = infinity Lens in water has larger focal length! n 1 <n 2

5. 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. Assumptions: monochromatic light incident on a thin lens. rays are all “near” the principal axis. Review: Converging Lens Principal Rays F F Object P.A. Image is real, inverted and enlarged Image

6. Physics 102: Lecture 19, Slide 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?

7. Physics 102: Lecture 19, Slide 6 Preflight 19.1 Java 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. Physics 102: Lecture 19, Slide 7 Java Preflight 19.1 Still see entire image (but dimmer)!

9. Lens Equation F F Object P.A. dodo didi f Image d o = distance object is from lens: Positive: object __________ lens Negative: object __________ lens d i = distance image is from lens: Positive: ________ image (behind lens) Negative: ________ image (in front of lens) f = focal length lens: Positive: ___________ lens Negative: ___________ lens d i = m =

10. Lens Equation F F Object P.A. dodo didi f Image d o = distance object is from lens: Positive: object in front of lens Negative: object behind lens d i = 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. Physics 102: Lecture 19, Slide 10 Amazing Eye One of first organs to develop. 100 million Receptors 4 million –200,000 /mm 2 2,500 /mm 2 –Sensitive to single photons! Candle from 12 miles Ciliary Muscles

12. Physics 102: Lecture 19, Slide 11 ACT: Focusing and the Eye Cornea n= 1.38 Lensn = 1.4 Vitreousn = 1.33 Which part of the eye does most of the light bending? 1) Lens2) Cornea3) Retina4) Cones Ciliary Muscles

13. ACT: Focusing and the Eye Cornea n= 1.38 Lensn = 1.4 Vitreousn = 1.33 Which part of the eye does most of the light bending? 1) Lens2) Cornea3) Retina4) 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 Ciliary Muscles

14. Physics 102: Lecture 19, Slide 13 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:

15. Physics 102: Lecture 19, Slide 14 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:

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

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

18. Physics 102: Lecture 19, Slide 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? 1) 13 cm 2) 26 cm 3) 52 cm Preflight 19.3

19. Physics 102: Lecture 19, Slide 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? 1) 13 cm 2) 26 cm 3) 52 cm 26cm 13cm Preflight 19.3 Image from mirror becomes object for eye!

20. Physics 102: Lecture 19, Slide 19 Multiple Lenses Image from lens 1 becomes object for lens 2 1 f1f1 f2f2 2 Complete the Rays!!

21. Physics 102: Lecture 19, Slide 20 Multiple Lenses: Magnification f1f1 f2f2 d o = 15 cm f 1 = 10 cm d i = 30 cm f 2 = 5 cm L = 42 cm d o =12 cm d i = 8.6 cm 12 Net magnification: m net = m 1 m 2

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

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

24. Physics 102: Lecture 19, Slide 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

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

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

27. Physics 102: Lecture 19, Slide 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?

28. Physics 102: Lecture 19, Slide 27 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? Farsighted person’s glasses are converging – like magnifying glass!

29. Physics 102: Lecture 19, Slide 28 Angular Size Preflight 19.6, 19.7 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? Highwire Caramel Apples Rabbits Kindergarten Hello Arboretum Halloween Amazing     Both are same size, but nearer one looks bigger.

30. Physics 102: Lecture 19, Slide 29 Unaided Eye Bring object as close as possible (to near point N) How big the object looks with unaided eye. ** If  is small and expressed in radians.  object N h0h0

31. Physics 102: Lecture 19, Slide 30 Magnifying glass produces virtual image behind object, allowing you to bring object to a closer d o : and larger  ’ Compare to unaided eye: : Ratio of the two angles is the angular magnification M: Magnifying Glass object virtual image hihi hoho didi dodo magnifying glass

32.  M lies between and the shorter the focal length, the greater the magnification M. Angular Magnification M=N/d o M = object virtual image hihi hoho dodo magnifying glass (N = near point distance from eye.) didi For max. magnification, need image at N, so set d i = -N:

33.  M lies between and the shorter the focal length, the greater the magnification M. = For max. magnification, need image at N: so set d i = -N: d i < -N Angular Magnification M=N/d o M = 25/10 + 1 = 3.5 object virtual image hihi hoho dodo magnifying glass (N = near point distance from eye.) didi

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