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Magnifiers, Projectors, Cameras Applied Optics Paul Avery University of Florida

Magnifiers, Projectors, Cameras Applied Optics Paul Avery University of Florida http://www.phys.ufl.edu/~avery/ avery@phys.ufl.edu Phy 3400 Light, Color and Holography. Magnifier. Consider small object held in front of eye Height y Makes an angle  at given distance from the eye

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Magnifiers, Projectors, Cameras Applied Optics Paul Avery University of Florida

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  1. Magnifiers, Projectors, Cameras Applied Optics Paul Avery University of Florida http://www.phys.ufl.edu/~avery/ avery@phys.ufl.edu Phy 3400 Light, Color and Holography Paul Avery (PHY 3400)

  2. Magnifier • Consider small object held in front of eye • Height y • Makes an angle  at given distance from the eye • Goal is to make object “appear bigger”: ' >  y  Paul Avery (PHY 3400)

  3. Magnifier • Single converging lens • Simple analysis: put eye right behind lens • Put object at focal point and image at infinity • Angular size of object is , bigger! Outgoingrays Rays seen comingfrom here y   f f Image atInfinity Paul Avery (PHY 3400)

  4. Angular Magnification (Standard) • Without magnifier: 25 cm is closest distance to view • Defined by average near point. Younger people do better •   tan  = y / 25 • With magnifier: put object at distance p = f • '  tan ' = y / f • Define “angular magnification” m = ' /  • Note that magnifiers work better for older people because near point is actually > 25 cm Paul Avery (PHY 3400)

  5. Angular Magnification (Maximum) • Can do better by bringing object closer to lens • Put image at near point, q = -25 cm • Analysis •   tan  = y / 25 • '  tan ' = y / p • m = ' /  = 25 / p Rays seen coming fromnear point. Can’t bringany closer! Outgoingrays y  f f Paul Avery (PHY 3400)

  6. Example • Find angular magnification of lens with f = 5 cm Paul Avery (PHY 3400)

  7. Size of Image from Magnifier • How big is projected image of sun? • Sun is 0.5 in diameter (0.0087 rad) • Image located at focal point. Why? • Size is f   = 5  0.0087 = 0.0435 cm • Energy 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) Paul Avery (PHY 3400)

  8. Projectors • Idea: project image of slide onto distant screen • Put slide near focal point of lens • Upside down to make image upright Paul Avery (PHY 3400)

  9. Projector Example • Projector problem • 5 cm focal length • 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 equation • So 5.085 cm from lens, just past focal point Paul Avery (PHY 3400)

  10. Camera • Lens projects image on film • Distance adjustment • Object at distance p • Film at fixed position • Fixed focal length f • Solution: move lens • Light adjustment • Shutter speed • Aperture setting • Film speed Camera: Film replaces eyeImage projected on film Paul Avery (PHY 3400)

  11. Other Details • Real cameras have several lenses • 6 lenses more common • Correct for various defects • Lens systems have equivalent focal length • “Standard” lens is 50 mm, i.e. f = 50 mm • Other lenses possible, e.g. 28 – 210 mm • 28, 35 mm lens are “wide angle” • > 50 mm are “telephoto” (100, 200, 300, 400, etc) • “Zoom” lenses allow variable f (using multiple lenses) • 35 – 105 mm • 28 – 80 mm • 70 – 210 mm • Film pressed flat against holder • Want film to form perfect plane perpendicular to optic axis Common varieties Paul Avery (PHY 3400)

  12. Spherical Aberration in Lenses • Thick lenses must be ground to accurate shape • Spherical is not the correct shape for best image Paul Avery (PHY 3400)

  13. Chromatic Aberration in Lenses n varies with  Correction requiresmultiple lenses Paul Avery (PHY 3400)

  14. Multiple Lenses in Cameras • Multiple lenses correct for various aberrations • Spherical aberration (poor focus at edge of lens) • Chromatic aberration (index of refraction varies with ) • Gauss arrangement probably most common • Actual arrangements are compromises! • No perfect corrections for all factors • Balance of many factors, including cost Paul Avery (PHY 3400)

  15. Variation of Index of Refraction Paul Avery (PHY 3400)

  16. Variation of Index of Refraction Paul Avery (PHY 3400)

  17. Single Lens Reflex (SLR) Cameras • You see exactly what film sees • Mirror, prism arrangement allows you to see • Mirror flips out of the way when shutter is pressed Paul Avery (PHY 3400)

  18. A Real SLR Camera! Paul Avery (PHY 3400)

  19. Image Size on Film • Example: 20 cm size object, 5 m distant • Use standard 50 mm lens (f = 50 mm) • Size easily calculated from geometry • Lens equation: q = 5.05 cm  f Paul Avery (PHY 3400)

  20. Image Size (cont.) • Image size proportional to focal length • Telephoto lenses are magnifiers • 100 mm lens makes 2 image • 200 mm lens makes 4 image • etc. • Telephotos and zoom lenses require stability • Shaking is also magnified • Require tripods, etc. Paul Avery (PHY 3400)

  21. f-number and Brightness • Define f-# = f / D • f = focal length • D = lens diameter • f-number defines brightness of image • Area of image  f 2 • Amount of light  D2 • Brightness  (D / f)2 = 1 / (f-#)2 • Camera settings allow x2 brightness change per step • Setting is 1.4 = 2 per step • 1.4, 2.0. 2.8 • 4.0, 5.6, 8 • 11, 16, 22 Paul Avery (PHY 3400)

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