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University of Wisconsin - Milwaukee

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Problem 4 Medium Difficulty

A digital camera equipped with an $f=50.0$ -mm lens uses a CCD sensor of width 8.70 $\mathrm{mm}$ and height 14.0 $\mathrm{mm}$ . Find the closest distance from the camera to a 1.80 -m-tall person if the person's full image is to fit on the CCD sensor.

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Video Transcript

and this problem. We have a camera with focal length of 15 millimetre that has a CCD sensor. The week of the CCD sensor is 8.7 millimeter and the height of the sea city is 14 millimeter and we have an object of height 1.8 meter equal to 1800 millimeter. So what we're trying to do is we're trying to find the object of stairs perfect object distance so that we can perfectly fit the image of the object at the CCD sensor. So we have to do a couple of things to be able to find that object. This is let's start with the definition of the magnification. So the the definition of the magnification, that magnitude of the magnification is H I over a So which is also D I over t o. And from here, actually, you can write down d I equals each eye over h o times. D'oh! So let's call this equation one. Now we're gonna use the lens equation and using the lens equation we can write down in his distance. D I calls t o times f over d o minus f. And let's call this equation too. All right, so from Equation One and Equation, too. Let's go back here to page one. You can see that D I equals H over H over time CEO and from prison to Diego's duo times f over to you myself. So if you solve this solving equation one into, we're going to get d'oh, that's going to be called to F inside the bracket h over h I plus one. So let's call this equation three. So now, to find the object distance, what we're going to do is we're going to plug in the values of focal length Asia and H i N Equation three. Okay, so we actually have two different cases. One is the portrait more and one is the landscape more so in portrayed, moored in portrait moored. Yeah, we have a chai because h i y. So from here using equation, too. It's our equation. Three dio is going to be cool to h o over h i Y plus one and this is going to be cool to 50 inside the bracket 1800 which was a a Y over 14 plus one, So 1800 was actually a so, um so from here, We're going to get 64 79 millimeter, which is approximately called to 6.48 meter. Okay, so next more is the landscape more okay for the landscape? More? What is gonna happen is a chai is going to be called Thio each i X So from here we'll get d o just similar way as portrait. More Dio is going to be culture 10 3 95 millimeter, which is equal to 10.4 meter.

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools

Zachary M.

Hope College