The Physics of Sight

1. The Physics of Sight Crystal Sigulinsky University of Utah: Interdepartmental Program in Neuroscience crystal.cornett@utah.edu

2. Objectives • Properties of Light • The Eye • Image Formation • Accomodation • The “-Opias” • Glasses • Review Questions

3. Sight Crystal Sigulinsky, 2007

4. Light • Electromagnetic radiation http://en.wikipedia.org/wiki/Image:EM_spectrum.svg

5. Properties of Light • Wave model • Classical sinusoidal wave • Unique in that can travel through a vacuum • Describes reflection, refraction, diffraction, interference, and Doppler Effect phenomena, etc. • Particle model • “photon” • Describes absorption and emission phenomena Image from http://en.wikipedia.org/wiki/Image:Wave.png

6. The eyes mediate sight • Function • Sensory organ for sight • Detects light and converts it into neural responses that the brain interprets http://en.wikipedia.org/wiki/Image:Eye_iris.jpg

7. Eye Anatomy • Anatomy • Light enters the eye through the pupil • Photoreceptors (light-sensing cells) are located in the retina • Retina acts like the film in a camera • GOAL: to focus the image on the back of the retina http://en.wikipedia.org/wiki/Eye How are images formed?

8. Image Formation: Apertures • Apertures • “openings” • Basis of a pinhole camera • Dark box • small “pinhole” to let in light • Image screen on opposite side of hole • All light rays from a scene pass through single point (focusing) http://en.wikipedia.org/wiki/Image:Pinhole-camera.svg Matthew Clemente; http://en.wikipedia.org/wiki/Image:Pinhole_hydrant_neg_pos.jpg

9. The Pupil is an Aperture • Pupil • Opening in the center of the eyeball • Bounded by the Iris • The iris controls the size of the pupil • Opening through which light enters the eye Pupil Iris http://en.wikipedia.org/wiki/Image:Eye_iris.jpg

10. Image Formation: Apertures • To achieve a clear image on an image screen, the aperture must be very small • Problems: • Smaller aperture: • Fewer photons get through • Dimmer image • Ratio of pinhole diameter to image distance should be less than 1/100 • Image screen must be large • Eye would have to be MASSIVE • Diffraction and Vignetting occur • Solution?? Small Aperture Large Aperture

11. Lenses are the Solution to the Aperture Problems • Lenses move the focus of the light waves past the aperture • Focuses the image on the screen • Allows for wider apertures • Produces smaller images Large Aperture Problem Modified from: http://en.wikipedia.org/wiki/Image:Lens3.svg Aperture & Lens Solution

12. Lenses of the Eye http://en.wikipedia.org/wiki/Eye

13. Focus Lenses of the Eye • Cornea • Crystalline Lens • Primary function • To focus the image on the back of the retina http://en.wikipedia.org/wiki/Eye Refractive power: Cornea = 39 - 48 diopters; Lens = 15 - 24 diopters

14. Refraction • Bending of the path of a light wave as it passes across the boundary separating two media • Cause: • Change in the speed of the light wave • No change in speed = no refraction! See Marching Soldiers Analogy Physics Classroom Tutorial: Refraction and the Ray Model of Light

15. Optical Density • Optical density of a material determines the speed of a wave passing through it • ↑ Optical density = ↓ Speed • How to remember this concept • Water is more dense than air • Harder to push yourself through water than air • Think of walking on ground (through air) versus in a pool (through water) • Harder, so you slow down

16. Index of Refraction • Abbreviated as “n” • Indicator of optical density • Indicates the number of times slower that a light wave would move through that material than it would in a vacuum.

17. Refraction: What direction? • FST = Fast to Slow, Towards Normal • Low optical density, low n to high optical density, high n • Light ray bends TOWARDS normal • SFA = Slow to Fast, Away from Normal • High n to low n • Light ray bends AWAY from normal See Marching Soldiers Analogy Physics Classroom Tutorial: Refraction and the Ray Model of Light Physics Classroom Tutorial: Refraction and the Ray Model of Light

18. Refraction: What direction? • What happens if you approach perpendicular to the boundary?? • NO refraction! • Light must approach the boundary at an angle for refraction to occur. See Marching Soldiers Analogy Physics Classroom Tutorial: Refraction and the Ray Model of Light Physics Classroom Tutorial: Refraction and the Ray Model of Light

19. Normal Θi Material A ni Material B nr Θr Refraction: How Much? • Snell’s Law • Quantitative answer to the question of “By how much does the light ray refract?” • ni*sine(θi) = nr*sine(θr) • ni = index of refraction of incident media • nr = index of refraction of refractive medium • θi = angle of incidence • θr = angle of refraction • **Angles are measured from normal Modeled after Physics Classroom Tutorial: Refraction and the Ray Model of Light • If ni = nr, then no refraction!!

20. Object-Image Relationship • Image location changes depending on object distance for a given lens’ focal length • The Lens Equation • 1/f = 1/dobject + 1/dimage Modeled after Physics Classroom Tutorial: Refraction and the Ray Model of Light

21. Problem • Retina is a fixed distance from the cornea-lens system (~22 mm or 2.2 cm) • Lens Equation • 1/f = 1/dobject + 1/dimage • In the eye, • dimage is fixed = distance between cornea lens system and the retina • dobject is fixed = distance between the eye and the object being viewed • Solution??

22. The Solution is Accomodation • Accomodation • The ability of the eye to change its focal length (f) • Mediated by the lens and ciliary muscles http://en.wikipedia.org/wiki/Eye

23. Nearby Objects Have a longer dimage Shorten the focal length Ciliary muscles contract Squeeze the lens into a more convex (fat) shape Pushes cornea bulge out further = greater curvature Distant Objects Have a shorter dimage Lengthen the focal length Ciliary muscles relax Lens assumes a flatter (skinnier) shape Cornea is not pushed out = less curvature Accomodation http://en.wikipedia.org/wiki/Image:Focus_in_an_eye.svg

24. Near Point • Closest point at which an object can be brought into focus by the eye • Ideally ~25 cm • Finger Experiment • Limited by the curvature of the cornea and adjustable radii of the lens • Recedes with age (can lead to farsightedness)

25. Far Point • Farthest point at which an object can be brought into focus by the eye • Typically is infinity • Decreases with age

26. Four-Color Women • Tetrachromats • 4 “color channels” • 4 types of cone cells, each containing a pigment responding to a unique wavelength set • Normal variation in cone pigment genes • “Orange” cone pigment • Only women • Red and green cone genes located on X chromosome • Normally X-inactivation occurs NOT on Exam – just for fun

27. Properties of Light Dual nature The Eye Anatomy Function Image Formation Apertures Lenses Refraction Will it occur? What direction? How much? Accomodation Object-Image Relationship Lens Equation Near point Far point Review

28. Hyperopia (Farsightedness) • INABILITY of the eye to focus on NEARBY objects • “Can see far” – no difficulty focusing on distant objects • Images of nearby objects are formed at a location BEHIND the retina • Near point is located farther away from the eye

29. Hyperopia: Causes • Shortened eyeball (retina is closer than normal to the cornea lens system) • Cornea is too flat • Lens can not assume a highly convex (fat) shape

30. Hyperopia: Correction • Need to refocus the image on the retina • Decrease the focal length of the cornea-lens system • Add a converging lens

31. Presbyopia • “After – 40” vision • Progressively diminished ability to focus on near objects as one ages • Similar to hyperopia, but different cause • Cause = diminished power of accomodation due to natural process of aging • Reduced elasticity of the lens • Weakening of the ciliary muscles • Changes in lens curvature due to continued growth http://en.wikipedia.org/wiki/Image:Specrx-accom.png

32. Myopia (Nearsightedness) • Inability of the eye to focus on DISTANT objects • “Can see near” – no difficulty focusing on nearby objects • Images of distant objects are formed in front of the retina • Far point is closer than normal

33. Causes of Myopia • Not usually caused by aging • Elongated eyeball (retina is farther away than normal from the cornea-lens system • Bulging cornea (greater curvature)

34. Correction of Myopia • Need to refocus the image on the retina • Increase the focal length of the cornea-lens system • Add a diverging lens

35. Astigmatism • Most common refractive error • Blurred or sometimes distorted vision at any distance • Cause: • Irregularly shaped cornea or lens • More oblong than spherical • Refractive power differs between regions • Correction • Glasses • Lenses with different radii of curvature in different planes

36. More info or clarification • crystal.cornett@utah.edu • The Physics Classroom Tutorial • http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/BBoard.html

37. Question # 1 Question: What is the eye? A. A sensory organ mediating the sense of sight B. A structure that detects light and converts it into neural responses that the brain interprets C. A structure whose anatomy is designed to focus light rays so that an image is formed on the back of the retina D. All of the above Answer: D. All of the above

38. Question # 2 Question: Converging lenses of the eye A. Include the cornea and crystalline lens B. Include the cornea and pupil C. Refract light rays to focus the image on the back of the retina D. Both A and B E. Both A and C Answer: E. The cornea and crystalline lens are the two lenses of the eye. The pupil is an aperture, not a lens, which allows light rays to pass through but does not refract them. The cornea-lens system refracts (bends) incident light rays to focus the image on the back of the retina

39. Question # 3 Question: Under what circumstances will refraction occur? A. When a light ray passes across any boundary B. When a light ray approaches at an angle to a boundary C. When a light ray changes speed due to entrance into a material of a different optical density D. A and B E. B and C F. All of the above Answer: E. Both B and C are true.

40. Question # 4 Question: What is the direction of refraction if the light wave crosses a boundary from a material with a high index of refraction (high n) into a material with a low index of refraction (low n)? A. Towards normal B. Away from normal Answer: B. Solution: high n = high optical density = slow low n = low optical density = fast If going from large n to small n, then going from slow to fast medium SFA = if go from Slow to Fast, then bend Away from normal

41. 60° Air (“n” = 1.0003) New Plastic (“n” = ?) 35° Question # 5 Question: You have created a new kind of plastic that is highly transparent and very resistant to scratching. It would make an excellent material for use in eye glasses. So, you need to know what the index of refraction is for this new material. You set up a simple experiment in which you measure the angles of incidence and refraction of a laser light as it passes from air (index of refraction is known) into the new plastic. What equation would you use to determine the index of refraction of your new plastic? A. Lens Equation B. Snell’s Law C. Angle Equation D. Refraction Law Answer: A. Snell’s Law

42. Question # 6 Question: Consider the phenomenon of accomodation. Under what condition do the ciliary muscles have to do the most work? A. When shortening the focal length of the cornea-lens system to view far off objects B. When lengthening the focal length of the cornea-lens system to view far off objects C. When shortening the focal length of the cornea-lens system to view objects that are near. D. When lengthening the focal length of the cornea-lens system to view objects that are near. Answer: C. The focal length of the cornea lens system must be shortened to focus the image of a near object on the back of the retina. This is achieved by contraction of the ciliary muscles that squeeze the lens into a more convex (fat) shape, which in turn pushes on the fluid in the chamber between the lens and cornea causing the cornea to bulge out further and have a greater curvature. The increased curvature of the cornea and more convex shape of the lens refract light rays more causing a shortening of the focal length of the system to bring near objects into focus. The longest focal length occurs when the ciliary muscles are relaxed during viewing of far off objects.

43. Question # 7 Question: If you took a fish out of water, would it exhibit hyperopia or myopia when trying to see in air? A. Hyperopia B. Myopia Answer: B. • Water has an index of refraction of 1.33 • Air has an index of refraction of 1.0003 • The index of refraction of the cornea-lens system is 1.37-1.4 • Both situations have light traveling from fast to slow so light rays will bend the same direction in both situations. • Going from air to the eye is a greater change in the index of refraction = greater change in angle of refraction • So image would form in front of the retina = Myopia

44. http://hyperphysics.phy-astr.gsu.edu/Hbase/vision/eyescal.htmlhttp://hyperphysics.phy-astr.gsu.edu/Hbase/vision/eyescal.html

45. Question # 8 Question: How does an optometrist correct for hyperopia? A. Equips the eye with a diverging lens to shorten the focal length of the cornea- lens system B. Equips the eye with a diverging lens to lengthen the focal length of the cornea- lens system C. Equips the eye with a converging lens to shorten the focal length of the cornea- lens system D. Equips the eye with a converging lens to lengthen the focal length of the cornea- lens system Answer: C. Hyperopia (farsightedness) occurs when the eye cannot focus on nearby objects because their images are formed behind the retina. To refocus the image on the retina, the focal length must be shortened. A shorter focal length is achieved by increasing the convergent refraction of the light rays and so a converging lens is added in front of the cornea lens system.