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Math Help - lens projection

  1. #1
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    lens projection

    A slide projector has a coverging lens whose focal length is 104.00 mm.
    (a) How far (in meters) from the lens must the screen be located if a slide is placed 108.70 mm from the lens?
    m

    (b) If the slide measures 24.0 mm 36.0 mm, what are the dimensions (in mm) of its image?
    mm x mm


    need help solving the lens problems please.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    A slide projector has a coverging lens whose focal length is 104.00 mm.
    (a) How far (in meters) from the lens must the screen be located if a slide is placed 108.70 mm from the lens?
    m

    (b) If the slide measures 24.0 mm 36.0 mm, what are the dimensions (in mm) of its image?
    mm x mm
    to (a): Use

    \frac1{d_O} + \frac1{d_I} = \frac1f

    Plug in the values you know:

    \frac1{108.7} + \frac1{d_I} = \frac1{104} . Solve for d_I . I've got: d_I \approx 2405.3\ mm

    So the distances of the screen from the lens should be 2.41 m

    to (b) Use

    Let O denote the length of the object (here: the measures of the slide) and I the length of the image:

    \frac IO = \frac{d_I}{d_O} . Plug in the values you know:

    \frac I{O} = \frac{2405.3}{108.7} \approx \underbrace{22.128}_{enlargement\ factor}

    Therefore 24\ mm \mapsto 531.1\ mm and 36\ mm \mapsto 796.6\ mm
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  3. #3
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    Okay, I kinda see how to plug them in now, but I was getting confused because I was reading d0 and d0- to mean the right or the left of the lens, and i didn't think I had that information. Even though its easily seen what the focal point is. Thanks for explaining the setup. Much more clear.
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