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A biology student uses a simple magnifier to examine the structural features of an insect’s wing. The wing is held 3.50 cm in front of the lens, and the image is formed 25.0 cm from the eye. (a) What is the focal length of the lens? (b) What angular magnification is achieved?

a. 4.07 \mathrm{cm}

b. 7.14

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University of Washington

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McMaster University

In this case, a student is trying to find the structural feature off an insect using magnifying Glynn's so the lenses actually held very close to thy. All right, So the first thing that we have here is the object distance that is a distance between the magnifying glass and insect. So let's write that down object just as P. He calls 3.5 centimeter and we actually have the m is distance, and that, actually is Q equals negative, 25 centimeter. So the reason why we have q goes negative 25 is because we are assuming that the lenses actually helped very close to thy, assuming that there is no actual distance between the lens and eyes. All right, so for the first case for the first case, which is part of a what we're gonna do is we're gonna try and find the focal length from here. The information we have here and if you use the lens equation, I'm gonna write this town directly using the lens equation. We can actually write down focal length. Half it caused P times Q over P plus que, and that is going to be 3.5 centimeter times negative. 2.5. Sorry. This is negative. 25 negative. 25 centimeter over 3.5. Plus negative. 25. All right, so from pure, we can get 4.7 centimeter. So the part first is done. Now let's go to part second. All right, so let's go to parse sigan. Now, when the lenses help very close to the eye. The angular magnification is maximum when the emails distance of the lenses at near point. And this exact this is exactly our case, right? So in this case, the angler magnification, actually. And Max. So actually, this one comes from the cuisine 25.5 from the textbook. The M Max is going to be called to one plus 25 centimeter over focal length. F story about that. So it's gonna be a Focal Inc path here, and we have all the information we need. One plus 25 centimeter over 4.7 sandy reader. And this will give us seven point 14 So this is the angular magnification

University of Wisconsin - Milwaukee