The Physics of Sight

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

2. Objectives • The eye • Image Formation • Apertures • Lenses • Accomodation • Nearsightedness and Farsightedness • Glasses

3. Sight

4. The eyes mediate sight • Function • Sensory organ for sight • Detects light and converts it into neural responses that the brain interprets

5. Eye Anatomy • Anatomy • Light enters through the pupil • Photoreceptors (light sensing cells) are located in the retina • Like the film in a camera • GOAL: to focus the image on the back of the retina

6. The Pupil is an Aperture • Apertures • “openings” • 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

7. Image Formation: Apertures • 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 • Focuses the light

8. Small Aperture Large Aperture Image Formation: Apertures • To achieve a clear image on an image screen, the aperture must be very small • Problems: • Image screen must be large • Eye would have to be massive • Smaller aperture results in a dimmer image • Less photons get through

9. 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 wider apertures • Produces smaller images Large Aperture Problem Aperture + Lens Solution

10. Lenses of the Eye • Cornea • Crystalline Lens • Primary function • To focus the image on the back of the retina

11. Refraction • Bending of the path of a light wave as it passes across the boundary separating two media • Caused by a change in the speed of the light wave • No change in speed = No change in direction of the line

12. 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

13. 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.

14. 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

15. 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 • If ni = nr , then no refraction!!

16. Refraction in Converging lenses

17. Lenses & Image Formation • Three Rules of Refraction for a Double Convex Lens • Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. • Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. • An incident ray which passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens. • Image is inverted (flipped horizontally over the principle axis)

18. Problem • Image location changes depending on object distance • Retina is a fixed distance from the cornea-lens system (~22 mm or 2.2 cm)

19. The Solution is Accomodation • The Lens Equation • 1/f = 1/dobject + 1/dimage • Accomodation • The ability of the eye to change its focal length (f) • Mediated by the lens and ciliary muscles

20. 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

21. Near Point • Closest point at which an object can be brought into focus by the eye • Finger Experiment • Limited by the curvature of the cornea and adjustable radii of the lens • Typically about 25 cm • Decreases with age

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

23. 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

24. Causes of Hyperopia • Shortened eyeball (retina is closer than normal to the cornea lens system) • Lens can no longer assume highly convex (fat) shape • Accomodation no longer working • Weakened ciliary muscles • Reduced flexibility of the lens • Common as people age

25. Correction of Hyperopia • Need to refocus the image on the retina • Decrease the focal length of the cornea lens system • More refraction • Add a converging lens

26. 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

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

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

29. Question # 1 Question: What is the eye? A. Sensory organ for 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 an image on the back of the retina D. All of the above Answer: D. All of the above

30. Question # 2 Question: How do apertures form images? A. By focusing light rays B. By refracting light rays C. By confining all rays from a scene through a single point D. Both A and B E. Both A and C Answer: E. confining all rays from a scene through a single point focuses these rays to form an image

31. Question # 3 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 aperature, 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

32. 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

33. Question: Calculate the angle of refraction (θr ) for the given boundary situation if the angle of incidence (θi) = 45 ° Answer: θr = 32 ° Solution -Use Snell’s Law: ni*sine(θi) = nr*sine(θr) Question # 5

34. Object 2F F F 2F Question # 6 • Using the 3 rules of refraction for a double convex lens, draw the image of the given object that would be formed by the following lens

35. Step 1. Determine the position of the image point corresponding to the top of the object (*) Step 2. Determine the position of the image point corresponding to the bottom of the object ($) 2F F F 2F Question # 6 (Solution) Object Object 2F F F 2F $ * *

36. Step 3. Fill in the image knowing that the * indicates the position of the top of the image and the $ indicates the position of the bottom of the image Correct Image Drawing Question # 6 (Answer) Object Object 2F F F 2F 2F F F 2F Image $ * Image

37. Question # 7 Question: What is involved in the accomodation for nearby objects (image distance is longer than the distance between the retina and the cornea lens system)? A. Focal length of the cornea lens system is shortened B. Ciliary muscles relax to make the lens skinnier C. Cornea has a greater curvature due to bulging D. A and C E. B and C Answer: D. The focal length of the cornea lens system must be shortened to focus the image 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

38. Question # 8 Question: How does an optometrist correct for hyperopia? A. Equips the eye with a diverging lens to increase refraction of light rays B. Equips the eye with a diverging lens to decrease refraction of light rays C. Equips the eye with a converging lens to increase refraction of light rays D. Equips the eye with a converging lens to decrease refraction of light rays 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 refraction of the light rays and so a converging lens is added in front of the cornea lens system.