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The actual light sensor size of a digital camera is 14.9 $\mathrm{mm} \times$22.3 $\mathrm{mm} .$ You want to take a photo of your friend, who is 1.9 $\mathrm{m}$tall. Your camera has a $55-\mathrm{mm}$ -focal-length lens. How far from the camera should your friend stand in order to produce a $22-\mathrm{mm}$ -tallimage on the light sensor?

4.80 $\mathrm{m}$

Physics 103

Chapter 27

Optical lnstruments

Wave Optics

Hope College

University of Winnipeg

McMaster University

Lectures

02:51

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Okay, so in this problem, your friend, uh, taking a picture, Let's see if they can't picture and he want we want to discover a reach distance off the camera. That means that these you know, he needs to stand so he can produce image off 22. You'll meet her stall. We know that the height off our friends is swamp 0.9 meters. And we know that the focal lens of the camera, it's just 55 of the meters. Okay, so how are we going to calculate this? We know from chapter 26 there is a way to combine distance and height using the magnification. So we know that distance of the image is just going to be miners magnification times zero. And we know the magnification is just height of the image, divided by height off the object. So combining this too, we have the distance off. The image equals to minors. H I divided by 80 times dessert. Okay, well, this is not enough to solve the problem because we do not have this sense of the image so we can use Phelan's a creation that is one divided by F. If course one divided by I lost. Oops, Sorry. One divided by zero. One divided by the zero. And we can substitute the d I that we have here. So this is going to be quote too. Let's see. One divided by F E clothes a zero divided by minus age. I do you zero well US one divided by zero. If we put these one divided by the zero evidence, we're going to have one divided by zero the multiplies one minus 80 divided by h i. So to blind is in cross. We have that, do you? Zero It's just going to be f multiplies one miners, 80 divided by age one. Now we can finally calculate inserted the distance. Okay, so substituting Oh, dividers we have here we have that The zero is 0.0 55 because we need to convert millimeters two meters. So this is going to be 0.0 55 times one miners, 1.9 divided by minus. Divided by minus 0.0 22. So this is just the zero equals to 4.8 meters. We put a minor sign in age I in here. If what this minor sign in here? Because the image is inverted. And when the image is inverted, we need to put a negative sign. The calculation. Therefore, the minus sign is there. Okay, so this is the final answer.

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