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Geometrical Optics Optical Systems Eyes Two Main Types: 1 Phys 322 Lecture 16 Chapter 5 Geometrical Optics Optical systems Eyes Two main types: 1. multifaceted (insects) 2. Single lens (animals) http://www.microscope-microscope.org/gallery/Kenn/kenn.htm Multifaceted eye Horsefly: 7000 segments Dragonfly: 30,000 segments Ants (some): 50 segments (Human: ~100,000,000 pixels) Eye resolution Human http://www.richard-seaman.com/USA/States/Illinois/VoloBog/LongLeggedFly9oClock.jpg Eye resolution Horse fly Human eye Human eye Most of the bending n1.376 Iris serves as aperture stop. Diameter changes from ~8 mm in dark to ~2 mm in bright light Note: it also contracts to increase sharpness when doing close work. collagen n1.337 (protein polymer) blind spot Floating specs (floaters): muscae volitantes http://en.wikipedia.org/wiki/Floater Crystalline lens of an eye Lens: 9x4mm, consists of ~22,000 layers of cortical fibers n = 1.386…1.406 http://www.bartleby.com/107/illus887.html http://www.owlnet.rice.edu/~psyc351/imagelist.htm Accommodation Far point: the object point whose 1 1 1 image lies on the retina for unaccommodated eye so si f 1 1 1 nl 1 f R1 R2 change focus Near point: the closest object point whose image could be projected on the retina with closest: accommodated eye young adult ~12 cm middle-aged ~30 cm 60 yrs old ~100 cm (Birds: change curvature of cornea) Physiological optics: dioptric power D 1 1 1 Instead of f use dioptric power D: D nl 1 f R1 R2 1 1 1 For 2 thin lenses closely spaced: D D1 D 2 f f1 f2 For intact unaccommodated eye D=58.6 D (Diopter) Far point: the object point whose image lies on the retina for unaccommodated eye Normal eye: far point is Nearsightedness (myopia) - far point is closer, D > 58.6 D Farsightedness (hyperopia) - far point is behind the lens, D < 58.6 D Near point: the closest object point whose image could be projected on the retina with accommodated eye Correcting vision Nearsighted eye and glasses Farsighted eye and glasses Example: nearsightedness (myopia) Far point is closer, D > 58.6 D Suppose far point = 2 m The additional lens must make the image si=-2 m for so= 2 m (assume lens-eye distance is small, contact lens) 1 1 1 1 1 Lens f = -2 m, or D=-0.5 D f so si 2m For spectacle lens distance d away from eyes: D l D Dl - distant lens power (d from eye) c 1 D d l Dc - equivalent contact lens power Astigmatism The lens has different radii of curvature in different planes test pattern: normal eye astigmatic eye http://www.thineyeglasses.com/glossary/astigmatism.htm Correction: cylindrical lenses More complex: sphero-cylindrical lenses Magnifying glass Purpose: enlarge a nearby object by increasing its image size on retina Requirements: • Image should not be inverted • Image should be magnified • Rays entering eye should not be converging Use positive lens and so < f Magnifying glass Magnifying power MP, or angular magnification - the ratio of the size of the retinal image as seen through the instrument to that as seen by bare eye at a normal viewing distance: - aided, - unaided MP a a u u Largest image without aid: Near point, do : closest point at which image can be Standard observer: do=0.25 m brought into focus Magnifying glass y / L MP a a i u u yo / do unaided view Using paraxial approximation aided view and lens equation (page 211): d MP o 1 D L l L 1 D f Most common case: so=f, L= Standard observer: MPL doD do=0.25 m If D=10, MP=2.5, notation 2.5X Typically limited to 2.5X - 3X Eyepiece (ocular) Eyepiece is essentially a magnifying glass that is designed to magnify image created by the previous optical system. Virtual object! Virtual image at Center of exit pupil - at eye plane More complex: The Huygens eyepiece Compound microscope ~1595, Zacharias Janssen: compound microscope ~1660, Robert Hooke’s microscope, ~30X magnification ~1700, Anton Van Leeuwenhoek microscope (single lens) 270X magnification “Father of microscope” Compound microscope Total magnification: MP = MTo MAe angular magnification of eyepiece Transverse magnification of objective Standard design: L = 160 mm Tube length Assuming standard tube length and standard viewing distance 25 cm: 160mm 250mm MP fo fe Respective powers are marked as 10X, 20X etc. Compound microscope Amount of light (brightness of image) depends on numerical aperture of the objective: NA = nisinmax Power = 40X NA=0.65 Maximum NA in air is 1 Can be as large as 1.4 - in oil Camera obscura Latin: dark room pinhole camera Portable tent version 1769 1620 1665:Vermeer The Girl with the Red Hat Probably used Inside camera obscura camera obscura Central Park, 1877 http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html Camera 1826: First photograph by Joseph Nicephore Niepce Exposure time: 8 hours! Modern SLR Camera single lens reflex For sharp image lens is moved back and forth - changing si changes so Film size is fixed (field stop) - changing f can change angular field of view. f=6-40 mm - wide-angle f~50 mm - normal angle f=80-1000 - telephoto lens Diaphragm=variable aperture stop controls f-number, or amount of light The telescope tele-skopos (Greek) - seeing at a distance 1608, Hans Lippershey tried to patent “kijker” “looker” (Dutch) 1609: Galileo, two lenses and an organ pipe Refracting telescope Notes: image is inverted object is typically at infinity f Angular magnification: MP a o u fe Terrestrial (non-inverting) telescope Binoculars Telescope aperture Telescope aperture: * determines amount of light collected more light - more low-brightness distant stars could be seen * determines the angular resolution diffraction limited angle is 1.22/D radians (chapter 10) - wavelength of light D - diameter of lens (or mirror) Exercise A friend tells you that the government is using Hubble telescope to read car license plates. Is it possible? Orbit height 600 km, aperture 2.4 m Hubble Assume best case scenario: the car’s license plate faces up Solution: To resolve license plate number need ~2 cm resolution 2 cm 1.22 500 nm must have D 20 m 600,000 m D 2.4 m telescope could resolve ~15 cm Note: atmospheric turbulence will most probably lower the resolving power below theoretical limit Refracting telescope aperture Largest refracting telescope (~1900): 40” doublet, 500 pounds. Net weight: 20 tons Yerkes, Williams Bay, WI http://www.wavian.com/aip/cosmology/tools/tools-refractors.htm Lens versus mirror: - harder to make (need large diameter to collect more light) - focal length depends on wavelength: n=n() Reflecting telescopes Keck 10 m telescope Hawaii, 1993 6 m single mirror telescope Russia: БТА-Большой телескоп азимутальный (1976) 42 tons 600 m radiotelescope Russia, Ратан-600 Reflecting telescope 1661: Invented by Scottsman James Gregory 1668: Constructed successfully by Newton prime focus Newtonian telescope Liquid mercury telescope z r Spinning liquid in equilibrium: parabolic surface 2r2 z 2g • One turn in ~10 seconds • must be maintained at 10-6 level Liquid mercury mirror • ~30 L of Hg for 6 m mirror 3m NASA’s Debris Observatory -7 • Surface smoothness ~10 (.3mm bump on Earth) • Points only up • Costs $1M instead of $100M 6 m liquid mercury telescope f/1.5 Zenith telescope 70 km East of Vancouver f/1.5, f=10 m mirror support http://www.astro.ubc.ca/LMT/lzt/gallery.html Correcting aberrations Spherical mirrors do not work: spherical aberrations and coma Catadioptric systems: Correct spherical aberrations Aplanatic reflectors: using specially profiled lens Both primary and secondary mirrors are hyperbolic Example: Hubble telescope Wavefront shaping Phys 322 Lecture 16 Lenses, mirrors - reshape wavefronts, designed to work with spherical or plane waves More complex elements - more complex wavefronts Wavefront distortions Light from star passes turbulent air - wavefront is not plane anymore, it has few m distortions (> ~0.5 m) In a good night, the planar area of the wave from distant star is ~20 cm - no matter how large the telescope is resolution is the same as that of 20 cm telescope! Need techniques that could constantly adapt optical elements to restore plane wave: Adaptive optics Adaptive optics Phase conjugation If we could at the same instant turn the wave direction backwards we can restore the initial (plane) wave shape The light propagation is reversible. 1972: Zeldovich et al. Use Stimulated Brillouin Scattering Intense electric field increases n at minima and maxima (sound wave) - constructive backward scattering (simplified view) /2.
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