PHY2054: Chapter 251Chapter 25: Applied OpticsPHY2054: Chapter 252Operation of the Eye24 mmPHY2054: Chapter 253Structure of the Eye Essential parts of the eye Cornea – transparent outerstructure Pupil – opening for light Lens – partially focuses light Retina – location of image Optic nerve – sends image tobrain Eye focuses light on retina Most refraction at cornea Rest of refraction at lensPHY2054: Chapter 254Iris Regulates Light Entering EyeThe 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 Eye Cornea-lens system focuses lightonto retina (back surface) Retina contains receptors calledrods (110M) and cones (7M) Rods & cones send impulses tobrain via optic nerve (1M fibers) Brain converts impulses into ourconscious 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 ConesOne type of rod Monochromatic vision Only used for night vision Highly sensitive3 types of cones 3 primary colors ⇒ color vision Not as sensitive as rodsPHY2054: Chapter 2510The Eye: FocusingDistant objects The ciliary muscle is relaxed Maximum focal length of eyeNear objects The ciliary muscles tenses The lens bulges a bit and the focal length decreases Process is called “accommodation”Focal length of eye (normal) f ≅ 16.3 mm 1/f ≅ 1 / 0.0163m = 60 “diopters” (= lens “power”) During accommodation, power (1/f) increasesPHY2054: Chapter 2511Example of Image Size on RetinaExample: A tree is 50m tall and 2 km distant. How big isthe image on the retina?2 km50 m16 mmh'5016 2000h!=0.4 mmh!=PHY2054: Chapter 2512The Eye: Near and Far PointsNear point is the closest distance for which the lens canaccommodate 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 > 25Far point is the largest distance for which the lens of therelaxed eye can focus light on the retina For normal vision, far point is at infinity (pfar = ∞) If nearsighted, then pfar is finitePHY2054: Chapter 2513Farsightedness (Hyperopia)The image focuses behind the retinaSee far objects clearly, but not nearby objects (pnear > 25 cm)Not as common as nearsightednessPHY2054: Chapter 2514Correcting FarsightednessA converging lens placed in front of the eye can correct hyperopia 1/f > 0, rays converge and focus on retinaExample: assume pnear = 200 cm = 2 m Goal: See object at 25 cm (normal near point) Strategy: For object at 25 cm, make image appear at near point1 1 1 1 14 0.5 3.5diopters0.25 2.0f p q= + = + = ! = +!PHY2054: Chapter 2515Nearsightedness (Myopia)See near objects clearly, but not distant objects (pfar < ∞)Most common condition (reading, etc)PHY2054: Chapter 2516Correcting Nearsightedness A diverging lens can be used to correct the condition 1/f < 0, rays diverge (spread out) and focus on retina Example: assume pfar = 50 cm = 0.5 m Goal: See objects at infinity (normal far point) Strategy: For object at infinity, make image appear at eye’s far point1 1 1 1 12.0diopt ers0.5f p q= + = + = !" !PHY2054: Chapter 2517Presbyopia and Age Presbyopia is due to a reduction inaccommodation range Accommodation range is max forinfants (60 – 73 diopters) Shrinks with age, noticeable effecton reading after 40 Can be corrected with converginglenses (reading glasses)PHY2054: Chapter 2518MagnifierConsider small object held in front of eye Height y Makes an angle θ at given distance from the eyeGoal is to make object “appear bigger” ⇒ Larger θyθPHY2054: Chapter 2519MagnifierSingle 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)Without magnifier: 25 cm is closest distance to view Defined by average near point (younger people can do closer) θ ≈ tanθ = y / 25With magnifier: put object at distance p = f Image at infinity θ' ≈ tanθ' = y / fDefine “angular magnification” mθ = θ' / θ2525y yfmf!! !!!""= =PHY2054: Chapter 2521Angular Magnification (Maximum)Can do better by bringing object closer to lens Put image at near point, q = −25 cmAnalysisθ ≈ tanθ = y / 25θ' ≈ tanθ' = y / pmθ = θ' / θ = 25 / pOutgoingraysRays seen coming fromnear point. Can’t bringany closer!θ′ff1 1 1251 1 12525 251p fp fmp f!+ ="= += = +yPHY2054: Chapter 2522ExampleFind angular magnification of lens with f = 4 cm256.3 Simple4251 7.3 Maximum4mm!!= == + =PHY2054: Chapter 2523Example: Image Size of MagnifierHow 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 cmEnergy 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 2524ProjectorsIdea: project image of slide onto distant screenPut slide near focal point of lens Upside down to make image uprightScreenLenspfqp f=!PHY2054: Chapter 2525Projector ExampleProblem Lens of 5 cm focal length Lens is 3 m from screen Where and how should slide be placed?Solution: real image required. Why?q = 3 m = +300 cm f = 5 cm Find p from lens equationSo 5.085 cm from lens, just past focal point1 1 1p f q= !( )( )300 55.085 cm300 5qfpq f= = =!
View Full Document
Unlocking...