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.. In a museum devoted to the history of photography, you are setting up a projection system to view some historical 4.0 inch $\times 5.0$ inch color slides. Your screen is 6.0 $\mathrm{m}$ from the projector lens, and you want the image to be 4.0 ft $\times 5.0$ ft on the screen. (a) What focal-length lens do you need? (b) How far from the lens should you put the slide?

a) $=46.2 \mathrm{cm}$b) 50 $\mathrm{cm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 25

Optical Instruments

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

University of Washington

University of Sheffield

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All right. So the question want was asking us to determine the focal lens off the subject here, okay of the project. So while we know that while vocalist is equal to one over image this it's minus one over. I'm sorry. While our object this is here, which is give us a focal dances equal to image this sometimes the object distance over the object business minus image Distance will just be you over humans meat. So he's given a 6.0 meter, which is the distance between the screen to the lens. OK, so in order to figure out the focal ends when you to figure out the object distance first. So it seems that we can do to question in one question. OK, so help me determine the object lands after distance. So there's another formula which is the formula off magnification which is equals m equal to minus B over you. You go to h cry over h H front Is the size off image A. She's the actual size. Okay, so this will give us you Is he for the minus V Over each cry over age, which is a good minds, we test h over h crime. And so now we know you is equal to minus fee times H over age of crime. Okay, so we know that age, which is the actual science. Let's just speak once I speak the four point oranges there. So the actual side of one side is 4.0, inches. Okay, Anyone? The side of image is equal to well going. Oh, feet. Okay. And remember that wifey is equal to 12 inches, which means that h over age crime is simply you go to four times the four point your inch over 4.0, times 12 inches. Unit will cancel out for four. Cancel. This will give us a jovic price one over. Troll A u is equal to minus fish off h prime, which will give us you is you go to minus fee times one over tall. Okay. Remember, he was given a 6.0 meters. So you is able to minus 6.0 meter times 1/2 and they sort of know why. While the tall and this will give us the object this is is equal to point. Oh, if I minus point over, I meter. Okay? which is negative 50 centimeters. So the question was only asking us how far run alleged do you put a slice? So only care about how far is it doesn't so it doesn't care about, is it on a map on the right, it's on the numbers matters in this case. So where needed Need the absolute very off the object since we just minus I mean sorry Absolutely you That was about you, which is absolute, very off connected 50 centimeter which will give us 50 centimeters. No, we know that you is equal to minus pulling over my meter, which is minus 50 centimeters and V is given as 6.0 meter. Remember, the focal ash was equal to the view over U minus we If we plug in a value, we'll get V was a six point old meter times the next 0.5 meter Okay, over U minus V, which is next 0.5 meter minus 6.0 meter. And this will give us the focal lens is equal to zero point 462 meaner. You become very two centimeter is 46 0.2 sending meter. Okay, so that's the answer for this question. And thank you

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