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Homework Help: Lens equation problem

  1. Dec 9, 2004 #1
    Hi my teacher assigned a few challenging optics problems, I got most of them but im stuck on this one..

    "Find a position on the principle axis that will ensure |hi| = ho ".

    When is the height of the image equal to the height of the object? How would I go about solving this?
  2. jcsd
  3. Dec 9, 2004 #2

    Doc Al

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    Staff: Mentor

    Another way to phrase the question: When is the linear magnification equal to 1 (or -1)?
  4. Dec 9, 2004 #3
  5. Dec 9, 2004 #4
    magnification equal to negative 1? how? ...........

    how can you have negative magnification? I understand the positive 1, and doesn't the absolute value bars around "hi" mean we're only concidering positive answers? ...

    Socceryjayl thanks for the website ... but lol I still don't know how they found 2F to be that point where hi = ho
  6. Dec 9, 2004 #5


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    Science Advisor
    Homework Helper

    Doc knows what he's talking about.The transversal linear magnification is defined by a ratio between two real numbers.As far as i know,such ratio should yield a positive number,or a negative one or zero.(In this special case,+-infinty is an accepted solution).In your case,for your relation to hold it could be as well "-1" as "+1".


    Show us your work,to see what u're doing wrong.
  7. Dec 9, 2004 #6
    lol I know Doc knows his stuff im not doubting him.

    ok well I used m = |hi|/ho to get m = 1.

    and m = -di/do, so 1 = -di/do ... I cross multiplied to get do = -di ........

    I subbed do = -di into the equation 1/do + 1/di = 1/f

    When I solved for f by doing -1/di + 1/di = 1/f

    I got 0 = 1/f ....

    But uhh... thats not a position on the principal axis, I dont see how they (in the website soccer gave me) they got 2F for the point where |hi| = ho
  8. Dec 10, 2004 #7

    Doc Al

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    The key is to realize that the heights will be equal when the distances are equal. Take a convex lens (f is positive) as an example. What condition will allow di = do? Using the lens equation: 1/di + 1/do = 1/f, so 1/do + 1/do = 1/f, thus do = 2f. This means that if we put the object at distance of 2f in front of the lens, the image will be a distance 2f behind the lens: and the heights will be equal. (In this case, m = - di/do = -1. The image is upside down.)
  9. Dec 10, 2004 #8
    Ohh I see, okay thanks...
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