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Homework Help: Optics and lens

  1. Oct 14, 2005 #1
    hey, i tried the following problem and i think i got it wrong well. here is the problem and what i did.

    problem
    A photograph of a zebra is taken from a distance of 100m with a 50mm lens. A second picture is taken from a distance of 50m with the same lens. What is the ratio of the height of the image in the second picture to the height in the first picture?

    What i did
    well. its obvious that the ratio is 2:1 because the distance of image int eh 100m to the distance of the 50m picture is 2:1 and the fact that it uses the same lens proves it. but my main issue with the problem is that i cant understand weather the 50mm lens can be used as the focal length of the problem. well I used it and here is what i got:

    for the 100m:
    1/f = 1/do + 1/di

    so: 1/0.050 = 1/100 + 1/di

    5di/0.050 = 5di/100 + 5di/di

    100di = 0.05di + 5

    100di - 0.05di = 5

    99.95di = 5

    99.95di/99.95 = 5/99.95

    Therefore: di = 0.050025012

    Note: to get the height of the image or object the equation is:

    M = hi/ho = -di/do

    I have the di and do but I don’t understand how I get hi or ho
    M is the magnification


    For the 50m:

    1/f = 1/do + 1/di

    So: 1/0.050 = 1/50 + 1/di

    2.5di/0.050 = 2.5di/50 + 2.5di/di
    50di = 0.050di + 2.5

    50di – 0.050di = 2.5

    49.95di = 2.5

    49.95di/49.95 = 2.5/49.95

    Therefore: di = 0.05005005

    ..here is the confusing part: the di of the 100 its half of the di or the 50 which I think it should be, and I don’t see how I can get the highet of the image.?
     
  2. jcsd
  3. Oct 14, 2005 #2

    Diane_

    User Avatar
    Homework Helper

    Would it help to point out that the height of the object remains the same in both cases?
     
  4. Oct 15, 2005 #3
    ok

    i know that the ho reamains the same but i dont know how i can show the relation between both cases? i dont understand how to get the ratio.

    edit: here is what i did..tell me if it is right

    case1
    hi/ho = 0.050025012/100

    hi/ho = 0.0005052012

    case2
    hi/ho = 0.05005005/50

    hi/ho = 0.001001001


    0.001001001/0.0005052012

    = 2.00100101 about 2

    therefore the ratio is 2:1

    is that right?
     
    Last edited: Oct 15, 2005
  5. Oct 16, 2005 #4
    so is it right?
     
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