Lecture #10

1. Lecture #10 Terrestrial eye optics 2/26/13

2. Why think about equations? • Understand physics of eye • Understand how variables affect each other • Get order of magnitude feel for things • Compare different organisms quantitatively • Test model for how something works • Shorthand

3. Where we are headed • HW#6 – Last one before midterm • Think about how mathematical modeling helps us understand vision • Midterm – 2 weeks from today • I will make equation sheet available next week that you will have for exam • Bring your sunglasses to class on Thursday

4. Transition to life on land • Transition from fish to tetrapods about 395 Mya Tiktaalik

5. Fish eye vs human Jobling 1995

6. Eyes above the surface • Aquatic eye in air • Lens focuses too much • First amphibians to crawl out of water would be myopic • Distant objects blurry • Close objects can be focused Fig 5.1

7. Aquatic to terrestrial transistion • Perfectly spherical lens with short focal length • Add focusing by the cornea

8. Eyes below the surface • Terrestrial eye in water • No cornea focusing • Land mammals that go back to water will not see in focus • - unless they are very myopic on land Fig 5.1

9. Today’s topics – Properties of terrestrial eyes • Optical power • Terrestrial eyes - bigger is better • Accomodation • Pupils • Ganglion cell densities

10. Optics interlude • Revisiting • Lens power • Lens focal lengths

11. Principle rays – help determine where image is located Nodal point

12. Eye has two focusing elements: Cornea and lens

13. Combine them into one effective focusing element Fig 5.3 Nodal point - effective center of curvature for combination of lens and cornea Any line from object through nodal point to image is straight - no refraction

14. Optics of objects and images Fig 5.3 f’ f • Object size is O Image size is I • Object distance U Image distance V • I / O = V / U • Magnification = I / O • Often <1 (demagnified) = f / U

15. Two different focal lengths – very confusing • Measured from nodal point • Measured from cornea

16. Focusing on land and in water • Lens in water and cornea in air have same power (do similar focusing) • For cornea • For symmetric aquatic lens

17. Physics lens equation Distance of image in relation to cornea/lens focal length O I U di

18. Physics lens equation Distance of image in relation to cornea/lens focal length O I U V This assumes air on all sides, nair=1

19. Physics lens equation Distance of image in relation to cornea/lens focal length n1 n2 O I U V Takes account of different n

20. Lens accomodation McIlwain fig

21. How your eye brings objects to focus U  di Squeeze lens f  di McIlwain An Intro to Biology of Vision

22. Far away object For object distance >3000 mm Image distance = 22.5 mm Focuses on retina Image distance for object far away Object distance

23. As move object closer to eye, image distance increases Object distances < 3000 mm Image distance 23.42 mm > 22.5 mm Focuses behind retina by 0.9 mm Image distance

24. As move object closer to eye, image distance increases As object gets closer, image goes further back behind retina Image distance

25. Point source of light At retina, image will be blurred Covers 0.12 mm of retina This is half the width of the fovea!

26. Point source of light Muscles squeeze lens to make it more rounded What happens to radius of curvature? What happens to f?

27. Point source of light Muscles squeeze lens to make it more rounded What happens to radius of curvature? What happens to f? Focal length shortens so image in focus on retina

28. Focusing

29. Focusing power • Power, P = 1/f • Units of optical power are dioptre (D) • Requires f be in meters • For human eye • f = 16.8 mm = 0.0168 m • Power = 1/0.0168m = 59.5 D

30. Focusing power P = 1/f • For two optical elements powers add f1=focal length of 1st element f2=focal length of 2nd element d=distance between elements n=index of refraction btn them

31. Power of each of the surfaces in human eye Cornea = 51.8 - 7.04 = 44.75 D This is a bit more than book says (40 D) Lens = 8.07 + 10.9 = 19 D

32. Terrestrial eye Split focusing power between cornea and lens Cornea 40 D : Lens 20 D 2 : 1 More surfaces of less curvature are better than one surface of high curvature Lower aberration

33. Myopia = near sighted • If person has 5 D of myopia • Glasses need to provide -5 D to correct the focus

34. Hyperopia • Far sighted • If person has 5D of hyperopia they need glasses with +5D to correct focus

35. Presbyopia • Eye is right shape • Lens no longer accomodates • Need +D to correct (1-4 D)

36. Astigmatism Radius of curvature of cornea (or lens) is different in two planes Correct with cylindrical or aspheric lens

37. Eyejusters – Next generation

38. Aquatic transition to terrestrial eye Optional ways for land animals to adjust Abandon lens - rely on cornea Keep spherical lens with flat cornea Keep both but shorten eye to match shorter focal length

39. Variety of terrestrial eyes Fig 5.6

40. 2. Terrestrial eyes: Bigger is betterTwo key traits of eyes • Sensitivity, S = 0.62 D2Δρ2Pabs • D = aperture • Δρ = receptor angle • Pabs = absorption probability • Resolution, 1/Δρ= f/d • f = lens focal length • d = receptor diameter

41. Terrestrial eyes vary with lifestyle Fig 5.7

42. Terrestrial eyes vary with lifestyle Nocturnal Large lens to gather a lot of light Short focal length so good sensitivity but not great resolution Fig 5.7

43. Terrestrial eyes vary with lifestyle Fig 5.7

44. Terrestrial eyes vary with lifestyle Long focal length Small aperture Good for resolution Fig 5.7

45. Terrestrial eyes vary with lifestyle Fig 5.7

46. Nocturnal vs diurnal

47. Largest eye of mammal

48. Largest eye of land animal

49. Eye size 150 mm 50 mm 40 mm 25 mm

50. Why have larger eye? #1 Resolution • Increase resolution by having longer focal length lens • Resolution = 1/Δρ= f /d