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A magnifying glass is a single convex lens with a focal length of$f=+14.0 \mathrm{cm} .$ (a) What is the angular magnification when thislens forms a (virtual) image at - $\infty$ ? How far from the object should the lens be held? (b) What is the angular magnification when thislens forms a (virtual) image at the person's near point (assumedto be 25 $\mathrm{cm}$ )? How far from the object should the lens be held inthis case?

a) 14.0 $\mathrm{cm}$b) 8.97 $\mathrm{cm}$

Physics 103

Chapter 27

Optical lnstruments

Wave Optics

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

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Okay, so and this problem, we have, uh, convex lens. Use it as a magnifying less. We know that this lens has, ah, focal lens off. 15. Let's see, 14 think emitters. 14 ST Emitters and their first item off the problem. We went to calculate the magnification m when the image is an infinity. So if the image is that infinity, we can say that the distance of the image is miners infinity. And we know from the chapter that the magnification toto magnification is just and divided by F when the image is a infinity. So in is near point off the off the lens, and the problem tells us that the near point that's put in here then your point is just 20 five centimeters and the focal ends is 14. You already know. So this needs to be equal to 1.8. So this is the magnification off this lens. Okay, a 2nd 1 what we went to calculate, we want to calculate how far the object needs to be held from the lens. So we went to discover the zero. Okay, so let's calculate this. The zero using the feelings equation just going to be one divided by F minus one divided by the I. All these to the power of minus one. We know that the distance off the images at infinity So this is simply one divided by f the power off minus one, which gives us 14. Same team enters. Oh, sir. So this is the end of the final answer to the first item. We have magnification off 1.8 and the distance of the object off farting sing team enters the second in the second item. We need to calculate the magnification when the image is that near point. Well, let's see, I can be the magnification when the image is that the near point is just one plus and divided by F. So this is just going to be one plus 25 divided by four things. So the magnification is just hopes. Sorry. So the magnification just going to be 2.82 point eight of magnification And what as we need to calculate, we need to calculate the object distance. The object distance indecent area, just one divided by F minus minors to minus one divided by the distance of the image reaches at the near point miners near point. So this is going to be one divided by 14. That is the focal int miners, one divided by minors, 25 the distance of the focal aunt. All of these to the power off minus one. So this needs to be equal to eight point 97 Same team enters, and that's your final answer. This problem.

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