Weekly Problems Feb 9 - Discussion Problems 3 Due in...

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Unformatted text preview: Discussion Problems 3 Due in section week of Feb 9, 2008 Quiz 3 One of the most ubiquitous applications of lenses is corrective glasses. First, one should know that the eyeball works like a converging lens. If you have good eyesight, then images should form on the retina. Suppose a person has trouble seeing an object which is 10 m away. You nd that with a corrective lens having a focal length -20cm = f1 (in gure) they can see well. Take the lens to sit 1cm away from the eye, as shown in the picture. Problem 1. So you want to be an ophthalmologist? a. For instructional purposes, lets say you know the person's eyeball has a focal length f2 = 1cm. Draw a ray diagram showing where the nal image will be. (Hint: rst draw the diagram for the image that would be formed by just the lens and then use this as a source for the eyeball.) b. Find the height and location of the image. How far in the eyeball is this person's retina? Figure 1: Lens with f1 are glasses, and the eyeball is represented by a lens of f2 . Problem 2. Learn the Lingo. a. At the eye-doctor you don't hear much about focal length. To see why, note that relative to most objects, your glasses sit very close to your eye. Given two lenses f1 and f2 immediately adjacent to each other, what is the eective focal length? b. Instead of focal length, doctors talk about a lens' power (for example, my prescription is -1.75, and bifocals can have -2 on one part and +1 for the other). The power of a lens is dened in such a way that putting two lenses together, it simply adds. In light of your answer from part a, how would you dene the lens' power? If the relevant dimension of lens power is some power of meters, what prescription does the person from question 1 need? 1 1 ...
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