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Understanding Lenses: Applications in Camera and Corrective Eyewear

Explore lenses in camera and corrective eyewear, lens power, near/far points, magnification, and angular sizes in this informative lecture review.

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Understanding Lenses: Applications in Camera and Corrective Eyewear

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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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