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PH 103

PH 103. Dr. Cecilia Vogel Lecture 8. Review. Lenses application to camera, eye application to corrective lenses. Outline. Lenses more corrective lenses angular size and magnification application to magnifier. Lens Power.

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PH 103

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  1. PH 103 Dr. Cecilia Vogel Lecture 8

  2. Review • Lenses • application to camera, eye • application to corrective lenses Outline • Lenses • more corrective lenses • angular size and magnification • application to magnifier

  3. Lens Power • Commented last time that a shorter focal length lens is stronger; • it causes the rays to change direction more. • Power of lens is defined as • Power = 1/f • To get power in Diopters (D), • use f in meters. • Your prescription will read in diopters.

  4. Near and Far Points • Near Point -- nearest distance your eye can focusclearly • Far Point -- farthest distance your eye can focusclearly • Wearing glasses changes your effective nearpoint/farpoint • Correcting distance vision makes near vision worse; • correcting near vision makes distance vision worse. 

  5. Nearpoint and Corrective Lenses • Suppose your near point without corrective lenses is N • and you wear lenses with focal length f<0 at a distance x from your eye. • What is the closest object you can clearly see when you are wearing these lenses? • REMEMBER that when you are looking THROUGH the lens, you are looking at the IMAGE, not the object!

  6. Nearpoint and Corrective Lenses • What is the closest object you can clearly see when you are wearing these lenses? • … one where the IMAGE is at distance N. • Given f and knowing di = -(N-x), we can find do • ex: farpoint = 2m, glasses 2 cm from eye (we found f=-1.98 m). suppose also N=10 cm w/o lens. New N=10.3 cm

  7. Angular size • Are stars big or small? • Angular size of object is angle object makes at your eye • depends on • size of object • distance away • tan(q) (size)/distance • tan(q)  q (in rad, if small) • q (size)/distance • qIN RAD

  8. Angular size • q (size)/distance • You can make an object seem bigger by bringing it closer • What’s the limit? • Limit = No closer than your nearpoint, N • (or you can’t see it clearly) • Largest angular size = size/N • = best you can do with naked eye

  9. Magnifying glass • Recall that reading glasses • make an image that is further, larger • than object. • Simple magnifier (aka magnifying glass) does the same thing • converging lens, case II, virtual image. • Image is larger, but… • it is also farther away, so… • it doesn’t seem any larger • ??

  10. Magnifying glass • How is a simple magnifier useful • if the larger image is farther away? • Usually one of two ways it is useful: 1. Suppose you need to spend long periods looking at objects up close • to see fine details. E.g. jeweler • Your eyes would get tired and strained. • Unless you use a lens to make the image farther away, so your eye can relax.

  11. Magnifying glass • How is a simple magnifier useful • if the larger image is farther away? • Usually one of two ways it is useful: 2. Suppose you would need to bring an object closer than your nearpoint • to see very fine details. • You can’t see the object that close clearly. • Unless you use a lens to make the image farther away, so your eye can see the IMAGE clearly.

  12. Angular magnification • What is angular size of image • compared to the best you can do with naked eye? • Angular size of image: • hi/|di| =ho/do • Angular size of object at your nearpoint • ho/N • this is the best you can do with naked eye

  13. Angular magnification • What is angular size of image compared to the best you can do with naked eye? • Angular size of image: ho/do • best you can do with naked eye • ho/N • So angular magnification is ratio of these • M = (ho/do)/(ho/N) M = N/ do General

  14. Angular magnification –special case: General: M = N/ do • What’s the easiest on the eye? • To have the image very far away • which means that do near f. • Relaxed-eye angular magnification • Mrelax = N/f

  15. Angular magnification –special cases: General: M = N/ do • What’s the best (biggest) you can get? • Put the IMAGE at your nearpoint, • di = -N • Find do from lens eqn, plug in above • Maximum angular magnification • Mmax = 1+(N/f)

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