PHY2054: Chapter 251Chapter 25: Applied OpticsPHY2054: Chapter 252Operation of the Eye24 mmPHY2054: Chapter 253Structure of the EyeÎ Essential parts of the eye Cornea – transparent outer structure Pupil – opening for light Lens – partially focuses light Retina – location of image Optic nerve – sends image to brainÎ Eye focuses light on retina Most refraction at cornea Rest of refraction at lensPHY2054: Chapter 254Iris Regulates Light Entering EyeÎThe iris is the colored portion of the eye A muscular diaphragm controlling pupil size (regulates amount oflight entering eye) Dilates the pupil in low light conditions Contracts the pupil in high-light conditionsPHY2054: Chapter 255Operation of EyeÎ Cornea-lens system focuses light onto retina (back surface) Retina contains receptors called rods (110M) and cones (7M) Rods & cones send impulses to brain via optic nerve (1M fibers) Brain converts impulses into our conscious view of the worldPHY2054: Chapter 256Picture of Retina (Seen Through Pupil)PHY2054: Chapter 257Rods Close Up (Retina Cross Section)PHY2054: Chapter 258Structure of Rods and ConesPHY2054: Chapter 259Color Perception in Rods and ConesÎOne type of rod Monochromatic vision Only used for night vision Highly sensitiveÎ3 types of cones 3 primary colors ⇒ color vision Not as sensitive as rodsPHY2054: Chapter 2510The Eye: FocusingÎDistant objects The ciliary muscle is relaxed Maximum focal length of eyeÎNear objects The ciliary muscles tenses The lens bulges a bit and the focal length decreases Process is called “accommodation”ÎFocal length of eye (normal) f ≅ 16.3 mm 1/f ≅ 1 / 0.0163m = 60 “diopters” (power of lens) During accommodation, f decreases and 1/f increasesPHY2054: Chapter 2511Example of Image Size on RetinaÎExample: A tree is 50m tall and 2 km distant. How big is the image on the retina?2 km50 m16 mmh'5016 2000h′=0.4mmh′=PHY2054: Chapter 2512The Eye: Near and Far PointsÎNear pointis the closest distance for which the lens can accommodate to focus light on the retina Typically at age 10, pnear~ 18 cm (use pnear= 25 cm as average) It increases with age (presbyopia) If farsighted, then pnear> 25ÎFar pointis the largest distance for which the lens of the relaxed eye can focus light on the retina For normal vision, far point is at infinity (pfar= ∞) If nearsighted, then pfaris finitePHY2054: Chapter 2513Farsightedness (Hyperopia)ÎThe image focuses behind the retinaÎSee far objects clearly, but not nearby objects (pnear> 25 cm)ÎNot as common as nearsightednessPHY2054: Chapter 2514Correcting FarsightednessÎA converging lens placed in front of the eye can correct hyperopia 1/f > 0, rays converge and focus on retinaÎExample: assume pnear= 200 cm = 2 m What we want: see object at 25 cm (normal near point) Strategy: put object at 25 cm, make image appear at near point 111 1 14 0.5 3.5diopters0.25 2.0fpq=+= + =− =+−PHY2054: Chapter 2515Nearsightedness (Myopia)ÎSee near objects clearly, but not distant objects (pfar< ∞)ÎMost common condition (reading, etc)PHY2054: Chapter 2516Correcting NearsightednessÎ A diverging lens can be used to correct the condition 1/f < 0, rays diverge (spread out) and focus on retinaÎ Example: assume pfar= 50 cm = 0.5 m What we want: see objects at infinity (normal far point) Strategy: if object at infinity, make image appear at eye’s far point1111 12.0diopters0.5fpq=+=+ =−∞−PHY2054: Chapter 2517Presbyopia and AgeÎ Presbyopia is due to a reduction in accommodation range Accommodation range is max for infants (60 – 73 diopters) Shrinks with age, noticeable effect on reading after 40 Can be corrected with converging lenses (reading glasses)PHY2054: Chapter 2518MagnifierÎConsider small object held in front of eye Height y Makes an angle θat given distance from the eyeÎGoal is to make object “appear bigger” ⇒ Larger θyθPHY2054: Chapter 2519MagnifierÎSingle converging lens Simple analysis: put eye right behind lens Put object at focal point and image at infinity Angular size of object is θ′, bigger!yθ′fImage at infinityq = ∞p = fPHY2054: Chapter 2520Angular Magnification (Simple)ÎWithout magnifier: 25 cm is closest distance to view Defined by average near point (younger people can do closer) θ≈tanθ = y / 25ÎWith magnifier: put object at distance p = f Image at infinity θ' ≈ tanθ' = y / fÎDefine “angular magnification” mθ = θ' / θ2525yyfmfθθθθθ′′==PHY2054: Chapter 2521Angular Magnification (Maximum)ÎCan do better by bringing object closer to lens Put image at near point, q= −25 cmÎAnalysisθ≈ tanθ= y/ 25θ'≈ tanθ'= y/ pmθ= θ' / θ = 25 / pOutgoingraysRays seen coming fromnear point. Can’t bringany closer!θ′ff111251112525 251pfpfmpfθ+=−=+==+yPHY2054: Chapter 2522ExampleÎFind angular magnification of lens with f= 4 cm256.3 Simple42517.3Maximum4mmθθ===+=PHY2054: Chapter 2523Example: Image Size of MagnifierÎHow big is projected image of sun? Sun is 0.5° in diameter (0.0087 rad) Image located at focal point. (Why?) Assume f = 5 cm Size is f×θ= 5 × 0.0087 = 0.0435 cmÎEnergy concentration of 10 cm lens? All solar rays focused on image Energy concentration is ratio of areas Concentration = (10 / 0.0435)2= 53,000! Principle of solar furnace (mirrors)fPHY2054: Chapter 2524ProjectorsÎIdea: project image of slide onto distant screenÎPut slide near focal point of lens Upside down to make image uprightScreenLenspfqpf=−PHY2054: Chapter 2525Projector ExampleÎProblem Lens of 5 cm focal length Lens is 3 m from screen Where and how should slide be placed?ÎSolution: real image required. Why?q= 3 m = +300 cm f = 5 cm Find pfrom lens equationÎSo 5.085 cm from lens, just past focal point111pfq=−()()300 55.085 cm300 5qfpqf==
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