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Chapter 27

Chapter 27. Lenses and Optical Instruments. Lenses. Converging lens. Diverging lens. Thin Lenses. A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane

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Chapter 27

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  1. Chapter 27 Lenses and Optical Instruments

  2. Lenses Converging lens Diverging lens

  3. Thin Lenses • A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane • Lenses are commonly used to form images by refraction in optical instruments

  4. Thin Lens Shapes • These are examples of converging lenses • They have positive focal lengths • They are thickest in the middle

  5. More Thin Lens Shapes • These are examples of diverging lenses • They have negative focal lengths • They are thickest at the edges

  6. Glass lens (nG = 1.52)

  7. The focal length of a lens is determined by the shape and material of the lens. Same shape lenses: the higher n, the shorter f Lenses with same n: the shorter radius of curvature, the shorter f Typical glass, n = 1.52 Polycarbonate, n = 1.59 (high index lens) Higher density plastic, n ≈ 1.7 (ultra-high index lens)

  8. Q. A parallel beam of light is sent through an aquarium. If a convex lens is held in the water, it focuses the beam (……..……………………. ) than outside the water nair = 1, nwater = 1.33 • closer to the lens • (b) at the same position as • (c) farther from the lens

  9. Rules for Images • Trace principle beams considering one end of an object • off the optical axis as a point light source. • A beam passing through the focal point runs parallel to • the optical axis after a lens. • A beam coming through a lens in parallel to the optical • axis passes through the focal point. • A beam running on the optical axis remains on the optical • axis. • A beam that pass through the geometrical center of • a lens will not be bent. Find a point where the principle beams or their imaginary extensions converge. That’s where the image of the point source.

  10. two focal points: f1 and f2 Parallel beams: image at infinite!!

  11. Virtual image Magnifying glass Virtual image

  12. 1/p + 1/q = 1/f Magnification, M = -q/p Negative M means that the image is upside-down. For real images, q > 0 and M < 0 (upside-down).

  13. Lens equation and magnification 1/p + 1/q = 1/f M = -q/p This eq. is exactly the same as the mirror eq. Now let’s think about the sign.

  14. 1/p + 1/q = 1/f 1/2f + 1/q = 1/f 1/q = 1/2f M = -q/p = -1 two focal points: f1 and f2 1/p + 1/q = 1/f 1/f + 1/q = 1/f 1/q = 0  q = infinite Parallel beams: image at infinite!!

  15. Virtual image Magnifying glass 1/p + 1/q = 1/f 2/f + 1/q = 1/f 1/q = -1/f M = -(-f)/(f/2) = 2 Virtual image

  16. positive f Ex. 27.1 A thin converging lens has a focal length of 20 cm. An object is placed 30 cm from the lens. Find the image Distance, the character of image, and magnification. f = 20, p = 30 1/q = 1/f – 1/p = 1/20 – 1/30 = 1/60 q = 60 real image (opposite side) M = -q/p = -60/30 = -2 < 0 inverted

  17. 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 

  18. 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

  19. 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 > 25cm ~y/25 ’~y/f M= ’/  = 25/f

  20. Example • Find angular magnification of lens with f = 5 cm

  21. Optical Instruments Eye Glasses Perfect Eye Nearsighted Nearsighted can be corrected with a diverging lens.  A far object can be focused on retina.

  22. Farsighted A Power of lens: diopter = 1/f (in m) (+) diopter  converging lens (-) diopter  diverging lens Larger diopter  Stronger lens (shorter f)

  23. Combinations of Thin Lenses • The image produced by the first lens is calculated as though the second lens were not present • The light then approaches the second lens as if it had come from the image of the first lens • The image of the first lens is treated as the object of the second lens • The image formed by the second lens is the final image of the system

  24. Combination of Thin Lenses, 2 • If the image formed by the first lens lies on the back side of the second lens, then the image is treated at a virtual object for the second lens • p will be negative • The overall magnification is the product of the magnification of the separate lenses

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