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Understanding Lenses and Imaging: Challenges and Solutions

Learn how lenses work in tandem and their uses in correcting and enhancing our view of the world. Explore the challenges of focusing an image using a single converging lens and discover the limitations of the human eye. Also, understand how multiple-lens systems can aid our vision.

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Understanding Lenses and Imaging: Challenges and Solutions

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  1. At this point, be sure that you have also read section 35.1 in the textbook—about how lenses work in tandem: The image produced by the first lens becomes the object that sends light to the next lens. Later, you should work through the After class 16 materials; and for more practice with multiple lenses, do Prep 5-6, items 4a, 4b and 4e. OSU PH 212, Before Class #16

  2. The real values of lenses and imaging, of course, are their uses: – They help to correct our view of the world (make it possible to view it clearly—i.e. “in focus”). – They help to enhance our view of the world (i.e. enlarge it for more detail). How do lenses perform these two tasks? It’s just like any other multiple-lens imaging systems; this system simply includes the converging lens that’s in your eye (it’s the last lens in the sequence): Light strikes the lenses in some order (first, second, third, etc.). The image produced by the first lens is the object for the next lens. OSU PH 212, Before Class #16

  3. A Challenge Suppose you’re trying to use a single converging lens to focus the image of some object on a screen in a room, under the following conditions: The room is small; most objects are larger than the room—and far from the room. The image distance—from the lens to the screen—is fixed (you can’t change it): di You can choose any converging lens focal length you wish, within a certain range: fmin ≤ f ≤ fmax At what nearest and farthest distances, do.min and do.max, could you place an object in front of the lens and still focus its image on the screen? OSU PH 212, Before Class #16

  4. This is the challenge of the human eye. The dimensions of the interior of the eyeball determine the image distance: di ≈ 2 cm The curvature of the cornea/lens system (which can change—but only within the limits of the muscles and lens tissue) determine the minimum and maximum focal lengths, fmin and fmax. Together, those factors determine the minimum and maximum object distances, do.min and do.max, at which we can achieve focused images of those objects. These limiting object distances, do.min and do.max, are called, respectively, the near point (NP) and far point (FP) of the eye. They define your eye’s focal range. OSU PH 212, Before Class #16

  5. Figure 24.6-2 OSU PH 212, Before Class #16

  6. Figure 24.8 OSU PH 212, Before Class #16

  7. For “normal” (average, unaided) eyes, the far point is essentially at infinity: FP = do.max ≈ . In other words: di ≈ fmax In a nearsighted eye (myopia), fmax is shorter than normal: di > fmaxThe eyeball is too long (the most relaxed lens is still too curved). The screen is too far from the lens for the lens’ maximum focal length, so the far point is nearer than infinity: FP <  In a farsighted eye (hyperopia), fmin is longer than normal: di < fmin. The eyeball is too short (the most curved lens is not curved enough). The screen is too close to the lens for the lens’ minimum focal length) so the near point is farther away than normal. For “normal” (average, unaided) eyes, NP is about 25 cm. Note what this says about a normal eye’s minimum focal length, fmin. OSU PH 212, Before Class #16

  8. Aiding the Eyes: Multiple-Lens Systems Allowing our eyes to focus: We can correct the physical flaws of our eyes (mismatched image distances and focal ranges) by using another lens to effectively change the object distance. How?We use the image of one lens (eyeglasses) as the object for the second lens (our eye). So we focus on that image instead of the original object. It’s all a matter of where that image is placed. For a near-sighted eye, we use a diverging lens to place an image of a distant object nearer, at that eye’s far point. See slide 9. For a far-sighted eye, we use a converging lens to place an image of a nearby object farther away, at that eye’s near point (slide 10). OSU PH 212, Before Class #16

  9. Figure 24.10 OSU PH 212, Before Class #16

  10. Figure 24.9 OSU PH 212, Before Class #16

  11. Assume that your eye’s far point (FP) and near point (NP) are normal (i.e. the standard distances; not needing any correction), and that the distance from your eye’s own lens to its retina is 2.00 cm. What are the maximum and minimum focal lengths (fmax and fmin) that your eye’s lens can achieve? A.fmax = 2.00 cm fmin = 1.85 cm B.fmax = –2.00 cm fmin = –2.17 cm C.fmax = ∞ fmin = 25.0 cm D. Not enough information E. None of the above. OSU PH 212, Before Class #16

  12. Assume that your eye’s far point (FP) and near point (NP) are normal (i.e. the standard distances; not needing any correction), and that the distance from your eye’s own lens to its retina is 2.00 cm. What are the maximum and minimum focal lengths (fmax and fmin) that your eye’s lens can achieve? A.fmax = 2.00 cm fmin = 1.85 cm B.fmax = –2.00 cm fmin = –2.17 cm C.fmax = ∞ fmin = 25.0 cm D. Not enough information E. None of the above. fhere is positive; your eye’s lens is a converging lens. And your FP and NP are objectdistances (do.maxanddo.min), not focal lengths. OSU PH 212, Before Class #16

  13. Now assume that your eye’s far point (FP) is 3.00 m but your near point (NP) is normal (and again, the distance from your eye’s own lens to its retina is 2.00 cm). What is the focal length of the lens you should wear next to your eye (a contact lens) so that you can view a star as a sharp pinpoint of light (rather than a fuzzy blur)? You may use ∞ for the star’s distance—that’s the object distance in this case. Hint: The corrective lens you’re wearing must bring its image to a location where it can then serve as the “object” for your eye’s lens. A.f = 3.00 m B.f = –3.00 m C.f = 1.99 cm D. Not enough information E. None of the above. OSU PH 212, Before Class #16

  14. Now assume that your eye’s far point (FP) is 3.00 m but your near point (NP) is normal (and again, the distance from your eye’s own lens to its retina is 2.00 cm). What is the focal length of the lens you should wear next to your eye (a contact lens) so that you can view a star as a sharp pinpoint of light (rather than a fuzzy blur)? You may use ∞ for the star’s distance—that’s the object distance in this case. Hint: The corrective lens you’re wearing must bring its image to a location where it can then serve as the “object” for your eye’s lens. A.f = 3.00 m B.f = –3.00 m (the lens’ image distance is negative—why?) C.f = 1.99 cm D. Not enough information E. None of the above. OSU PH 212, Before Class #16

  15. Now assume that your eye’s far point (FP) is 3.00 m but your near point (NP) is normal (and again, the distance from your eye’s own lens to its retina is 2.00 cm). What is the focal length of the eyeglasslens you should wear 2.00 cm from your eye so that you can view a star as a sharp pinpoint of light (rather than a fuzzy blur)? You may use ∞ for the star’s distance—that’s the object distance in this case. Hint: The corrective lens you’re wearing must bring its image to a location where it can then serve as the “object” for your eye’s lens. A.f = –3.02 m B.f = –3.00 m C. f = –2.98 m D. Not enough information E. None of the above. OSU PH 212, Before Class #16

  16. Now assume that your eye’s far point (FP) is 3.00 m but your near point (NP) is normal (and again, the distance from your eye’s own lens to its retina is 2.00 cm). What is the focal length of the eyeglasslens you should wear 2.00 cm from your eye so that you can view a star as a sharp pinpoint of light (rather than a fuzzy blur)? You may use ∞ for the star’s distance—that’s the object distance in this case. Hint: The corrective lens you’re wearing must bring its image to a location where it can then serve as the “object” for your eye’s lens. A.f = –3.02 m B.f = –3.00 m C. f = –2.98 m(this lens’ image distance is 2 cm shorter—why?) D. Not enough information E. None of the above. OSU PH 212, Before Class #16

  17. Now assume that your eye’s far point (FP) is normal, but your near point (NP) is 75.0 cm (and again, the distance from your eye’s own lens to its retina is 2.00 cm). What is the focal length of the eyeglasslens you should wear 2.00 cm from your eye so that you can hold a newspaper at the standard near-viewing distance (25.0 cm)? Hint: The corrective lens you’re wearing must bring its image to a location where it can then serve as the “object” for your eye’s lens. A.f = 33.6 cm B.f = 18.8 cm C. f = 37.5 cm D. Not enough information E. None of the above. OSU PH 212, Before Class #16

  18. Now assume that your eye’s far point (FP) is normal, but your near point (NP) is 75.0 cm (and again, the distance from your eye’s own lens to its retina is 2.00 cm). What is the focal length of the eyeglasslens you should wear 2.00 cm from your eye so that you can hold a newspaper at the standard near-viewing distance (25.0 cm)? Hint: The corrective lens you’re wearing must bring its image to a location where it can then serve as the “object” for your eye’s lens. A.f = 33.6 cm (do = 23.0 cm; di = –73.0 cm Why?) B.f = 18.8 cm C. f = 37.5 cm D. Not enough information E. None of the above. OSU PH 212, Before Class #16

  19. A vision correction summary (all lengths given here in cm): Near-sightedness: NP normal (≤ 25 cm) but FP too short (< ∞): Correction: A diverging lens with focal length f, such that 1/f = 1/∞ + 1/–(FP) (contact lens) 1/f = 1/∞ + 1/–(FP – 2) (eyeglasses) Far-sightedness: FP normal (∞) but NP too long (> 25 cm): Correction: A converging lens with focal length f, such that 1/f = 1/25 + 1/–(NP) (contact lens) 1/f = 1/23 + 1/–(NP – 2) (eyeglasses) OSU PH 212, Before Class #16

  20. And this vision correction terminology: Refractive Power (R.P.) has units of Diopters, which are m–1. Examples: A lens with a focal length of +40.0 cm has an R.P. of 2.50 D. A lens with an R.P. of –3.25 D has a focal length of –30.8 cm. OSU PH 212, Before Class #16

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