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Aiding the Eyes: Multiple Lens Systems

Learn how multiple lens systems can correct the physical flaws of our eyes and improve our vision. Discover how these systems allow us to focus better and see more detail by manipulating the placement and size of images formed on the retina.

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Aiding the Eyes: Multiple Lens Systems

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  1. Aiding the Eyes: Multiple-Lens Systems Allowing our eyes to focus (we covered this on Monday): We can correct the physical flaws of our eyes (the 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). We focus on that image instead of the original object. It’s all a matter of where that image is placed. For a nearsighted eye, we use a diverging lens to place a (virtual) image of a distant object nearer—at that eye’s far point. For a far-sighted eye, we use a converging lens to place a (virtual) image of a nearby object (25 cm) farther away—at that eye’s near point. OSU PH 212, Before Class #17

  2. Aiding the Eyes: Multiple-Lens Systems (2) Allowing our eyes to see detail (today’s topic): Even if we’re successful in focusing an image on our retina, we won’t see much detail if that image is too small—if it stimu- lates only a few cells on the retina. Can we make it bigger—still keep it sharply focused on the retina’s “screen,” but cover more area of the retina, firing more cells so that we can see more detail? Yes. This is what angular magnification is all about. Again, we use the image formed by external lenses as the object for the final lens (our eye). We focus on that image rather than the original object. It’s all a matter of how large that image is—and, as always, where it is placed. OSU PH 212, Before Class #17

  3. Figure 24.11A OSU PH 212, Before Class #17

  4. Angular Magnification The thin-lens and magnification equations tell us how big an image is and where it’s formed by any one lens. (And we can use more than one lens—the first image becoming the object for the second lens.) But how big does an image look—to your eye? In other words, how large an image does your eye’s lens finally form on your retina? That apparent size is really a matter of the angle the object subtends (occupies) in your view—which is the same angle it then subtends on your retina. This is called the angular size () of the object, and if we measure it in radians, we know this:  = tan-1(ho/do) ≈ (ho/do) OSU PH 212, Before Class #17

  5. The largest angle at which your unaided eye can view a focused object is when that object is located at your eye’s near point, do.min (a distance called NP). Placing the object at that distance NP from your eye produces the largest possible unaided image onto your retina: unaided ≈ (ho/NP) But you can aid your eye by magnifying the angular size of the ob-ject, using other lenses. You can create an image to view instead— an image which: (i) you can still focus on (it’s somewhere between your near point, NP, and your far point, FP) and (ii)subtends a larger angle in your eye than the object does: aided ≈ (hi/di) ≈ (ho/do) How much better is the detail now? A good measure, M (the angular magnification), is the ratio of these viewing angles (which, after all, gives the increase in “retinal coverage”): M = aided/unaided OSU PH 212, Before Class #17

  6. Figure 24.11 OSU PH 212, Before Class #17

  7. The Magnifying Glass If an object is just inside the focal point of a converging lens, the re-sulting image is upright (m > 0), virtual (di < 0), and larger than the object (m > 1). The image will form a larger angle (and thus a larger image on your retina); it will look bigger—and you’ll see more detail. How to measure the angular magnification, M? Compare the angle  made by the object (as placed at the near point, NP, where you see it “biggest” with your unaided eye) to ’, the angle made by the image (wherever the lens locates it—and with your eye viewing that image from right behind the lens): M = ’/ ≈ |(hi/di)|/(ho/NP) A little algebra: M ≈ (1/f – 1/di]·NP So M depends on where the image is (di); it must still be between your near and far points. You see most detail if the image is at your near point, NP (i.e. when di = –NP), in which case M ≈ NP/f + 1. OSU PH 212, Before Class #17

  8. Figure 24.12 OSU PH 212, Before Class #17

  9. A Summary of Angular Magnification Definition: M = q’/q The value of M as calculated for common instruments: Magnifier, “comfort” (standard) viewing: M ≈ NP/f Magnifier, maximum (strained) viewing: M ≈ NP/f + 1 Microscope, “comfort” (standard) viewing: M ≈ –NP(L – fe)/(fo·fe) Telescope, “comfort” (standard) viewing: M ≈ –fo/fe Note: Some of these instrument “ratings” are different (more general) than those presented in the textbook. For a more detailed summary and discussion of the differences (and why we’ll be using the above), be sure to read After Class 17. OSU PH 212, Before Class #17

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