Monocular Vision The Human Eye
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1 6.0 The Human Eye The human eye operates very much like a modern electronic camera Iris: controls the amount of light energy entering the lens Lens: focus light onto retina (adjustable) refraction also provided by cornea + A.H. Retina: Layer of electronic (ok neural) pixel elements Monocular Vision The lens focuses some of the rays ( emitted in all directions) from points on the pencil (the object) on to individual points (the image) on the retina The electrical impulses are carried by the optic nerve into the brain for processing shapes and colors
2 6.0 The Human Eye Muscles in the eye changes the shape (focal length) of the lens in response to near and far objects depth perception with just one eye This is a skill learned by a baby in the first few days after birth. It is difficult to demonstrate it is so automatic () Cover one eye. Stare at this screen with other eye. Then move a finger into field of view. () Cover one eye. Look down at one finger. Raise your head until this screen comes into field of view relaxed lens tensed lens Binocular Vision (a) Eyeballs rotate to center the object in each eye (conscious but fairly automatic response by the brain) more depth perception () Put one finger from each hand in front of you one at twice the distance of the other. () Alternately focus on one finger the other will be seen in double (b) The slightly different images seen in the two eyes are interpreted by the brain to given even more depth perception 3D glasses!
3 6.0 The Human Eye Relaxed Eye Lens Nearsightedness Distant D Object F (non-standard notation) (myopia) Far Point of nearsighted eye Image formed in front of retina Ideally, the lens of the eye should be able to adjust to objects at any distance. But the nearsighted eye has a lens-retina combination that cannot relax itself enough to focus objects out to infinity. A distant object focus to a real image in front of (but missing) the retina. Usually there is a maximum object distance, called the far point, to which the eye can focus Distant Object Distant Object d o Far Point of nearsighted eye Virtual Image formed by diverging lens Far Point of nearsighted eye Image formed on the retina Diverging Lens D L Corrective Lens The patient is prescribed a diverging lens to compensate for the over-convergence Prescription We want to put the virtual image made by the diverging lens of a distant object (i.e. d o ) at the far point: D F. Remember that the corrective lens is worn at a small distance D L in front of the eye (D L 0 for a contact lens) d i ( D D ) F L f + d o d i + f ( D L ) ( D ) F D F D L 3
4 6.0 The Human Eye With this prescription, objects at finite, but far distances are mapped into virtual images located between the corrective lens (at distance D L from the eye) and the far point (at distance D F from the eye) Example : Eyeglasses for the Nearsighted Person A nearsighted person has a far point located only 5 cm from the eye. Assuming that eyeglasses are to be worn cm in front of the eye, find the focal length needed for the diverging lens of the glasses so the person can see distant objects. 4
5 6.0 The Human Eye Example : Eyeglasses for the Nearsighted Person A nearsighted person has a far point located only 5 cm from the eye. Assuming that eyeglasses are to be worn cm in front of the eye, find the focal length needed for the diverging lens of the glasses so the person can see distant objects. f With this prescription, objects at finite, but far distances are mapped into virtual images located between the corrective lens (at distance D L from the eye) and the far point (at distance D F from the eye) d o + d i D F D L DF D L 5cm cm f 59 cm THE REFRACTIVE POWER OF A LENS THE DIOPTER Optometrists who prescribe correctional lenses and the opticians who make the lenses do not specify the focal length. Instead they use the concept of refractive power. Refractive Power ( RP : in diopters) f ( in meters) RP is not a standard notation, and diopter is not an SI unit. f 59 cm RP 093. m dpt 5
6 6.0 The Human Eye Near Point of nearsighted eye D N Close-by object Tensed Eye Lens (non-standard notation) Sharp image formed behind the retina Farsightedness (hyperopia) Ideally, the lens of the eye should be able to adjust to objects at any distance. But the Farsighted eye has a lens-retina combination that cannot tense itself enough to focus objects close by. A close-by object focus to a sharp, real image behind (but missing) the retina. Usually there is a minimum object distance, called the near point, to which the eye can focus Near Point of nearsighted eye Virtual Image formed by converging lens Near Point of nearsighted eye Close-by object Close-by object Converging Lens Converging Lens D L Sharp image on retina Corrective Lens The patient is prescribed a converging lens to compensate for the underconvergence Prescription Put the virtual image made by the converging lens of the nearest object you want to see (typically at D MIN 5 cm) to the near point: D N. RP f + d o d i ( D MIN D L ) ( D N D L ) 6
7 Example of corrective lens for farsightedness: this is a pathology everyone gets as they get older starting at ~40 yrs of age (nearsightedness improves somewhat in combination with this) Your professor wears reading glasses with refractive power of RP.75 dpt.75 m -. Where is his near point (inside of which he cannot see). Assume the glasses to correct for objects as near as 5 cm, and that the glasses are worn cm from the eyes. 7
8 Example of corrective lens for farsightedness: this is a pathology everyone gets as they get older starting at ~40 yrs of age (nearsightedness improves somewhat in combination with this) Your professor wears reading glasses with refractive power of RP.75 dpt.75 m -. Where is his near point (inside of which he cannot see). Assume the glasses to correct for objects as near as 5 cm, and that the glasses are worn cm from the eyes. RP f + d o d i ( D MIN D L ) ( D N D L ).75 m (0.5 m 0.0 m) ( D N 0.0 m) ( D N 0.0 m) 0.3 m.75 m.60 m D N 0.0 m.60 m 0.38 m D N 0.40 m 8
9 6. Angular Magnification and the Magnifying Glass The eye is basically like a camera The size of the image on the retina determines how large an object appears to be. θ ( in radians) Angular size h d o o 9
10 6. Angular Magnification and the Magnifying Glass Example: A Penny and the Moon Compare the angular size of a penny held at arms length with that of the moon. 0
11 6. Angular Magnification and the Magnifying Glass Example: A Penny and the Moon Compare the angular size of a penny held at arms length with that of the moon. Penny θ h d o o.9 cm 7cm 0.07 rad Moon θ h d o o m m rad
12 6. Angular Magnification and the Magnifying Glass Angular magnification M θ θ Angular magnification of a magnifying glass M f d i N
13 6. The Compound Microscope To increase the angular magnification beyond that possible with a magnifying glass, an additional converging lens can be included to premagnify the object. Angular magnification of a compound microscope M ( L f ) f o f e e N 3
14 Chapter 7 Interference and the Wave Nature of Light 4
15 7. The Principle of Linear Superposition When two or more light waves pass through a given point, their electric (and magnetic) fields combine (interfere) according to the principle of superposition. Special Case Special Case The waves emitted by the sources start out in phase and arrive at point P in phase, leading to constructive interference. m mλ 0,,,3, The waves emitted by the sources start out in phase and arrive at point P in opposite phase, leading to destructive interference. m ( m + ) 0,,,3, If constructive or destructive interference is to continue ocurring at a point, the sources of the waves must be coherent sources. Two sources are coherent if the waves they emit maintain a constant phase relation. 5 λ
16 7. Young s Double Slit Experiment Two independent, coherent light sources are virtually impossible to construct. In Young s experiment (Young also participated in the deciphering of the Rosetta Stone), two slits illuminated by a single source acts as two separate but coherent sources of light. Light waves from these slits interfere both constructively and destructively on the projection screen. For best results, light of a single color (e.g. produced by a laser) is used. The waves coming from the slits interfere constructively or destructively, depending on the difference in distances between the slits and the screen. 6
17 7. Young s Double Slit Experiment In the typical set up, the screen is very far away compared to the separation of the slits. We treat the rays from the slits as if they were parallel Bright fringes from slits sinθ m λ d Bright fringes Dark fringes d sinθ d sinθ mλ d sinθ ( m + ) λ m 0,,,3, Dark fringes from slits Bright fringe Dark fringe λ ( m ) d sin + θ m Bright fringe Dark fringe Bright fringe 7
18 7. Young s Double Slit Experiment Example: Young s Double-Slit Experiment Red light (664 nm) is used in Young s experiment with slits separated by d m. The screen is located a distance.75 m from the slits. Find the distance on the screen between the central bright fringe and the third-order bright fringe. θ m sin m λ sin 3 4 d.0 0 m 0.95 (.75 m) tan( 0.95 ) m y L tan θ Note: Double slit interference also separates out the colors from a white or multi-colored source. The angle of the bright fringes is different for each wavelength the bright fringes for different colors form a rainbow on screen. 8
19 7.3 Thin Film Interference Because of reflection and refraction, (at least) two light waves enter the eye when light shines on a thin film of gasoline floating on a thick layer of water. Because of the extra distance traveled by ray [] relative to ray [], there can be interference between the two waves. For the comparison of the extra path to wavelength, we need to use the wavelength in the medium λ film λ n vacuum film When light travels through a material with a smaller refractive index towards a material with a larger refractive index, (partial) reflection at the boundary occurs along with a phase change that is equivalent to one-half of a wavelength in the film. When light travels from a larger towards a smaller refractive index, there is no phase change upon reflection. 9
20 7.3 Thin Film Interference Example Color of a Thin Film of Gasoline A thin film of gasoline floats on a puddle of water. Sunlight falls perpendicularly on the film and reflects into your eyes. The film has a yellow hue because destructive interference eliminates the color of blue (469 nm) from the reflected light. The refractive indices of the blue light in gasoline and water are.40 and.33. Determine the minimum non-zero thickness of the film. Ray []: reflection at point A from lower to higher index: phase shift equivalent to ½ λ film λfilm A B Ray []: reflection at point B from higher to lower no phase shift ; but roundtrip through film: t Effective path difference between Ray [] and Ray [] (including phase shift for reflection) t λfilm Destructive interference between Ray [] and Ray []: difference of half-integer wavelengths t λfilm, λfilm, 3λfilm... t λ film, 3 λ λ film film, 5 λ film... Minimum non-zero thickness t : t λ 469 nm.40 film 68 nm 0
21 7.3 Thin Film Interference The wedge of air formed between two glass plates causes an interference pattern of alternating dark and bright fringes. Thin-film band-pass optical filter y Dark Fringes λ y ( m + ) λ mλ 0,,,3 Bright Fringes... m As long as the film has the highest refractive index of the three regions, then neither of the two reflections incur a phase shift. t Constructive interference between transmitted ray [] and ray [] occurs for the minimum thickness of t λfilm
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