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Magnification equation problem

  1. Feb 11, 2013 #1
    1. The problem statement, all variables and given/known data
    When an object is closer to a concave mirror than the mirror's focal point the...
    (a) Magnification is more than 1
    (b) Magnification is less than 1

    2. Relevant equations
    M = -Si/S
    1 / f = (1 / S) + (1 / Si)

    M = Magnification
    S = Distance between object and mirror
    Si = Distance between image and mirror
    f = Distance between focal point and mirror

    3. The attempt at a solution
    I an attempt to solve this problem i simply plugged in values where S<f, in this case i'll use S=1 and f=2.

    Plugging these values into the second equation i receive: 1/2 = (1/1) + (1/Si). From this equation i get Si=-2, and then plugging S=1 and Si=-2 into the second equation i get: M = -(-2/1) which is M = 2.

    If M=2 this leads me to believe that the answer to this question is (a), but according to the answers provided it should be (b). I really can't figure out where I've made a mistake. Any help would be much appreciated :)
     
    Last edited: Feb 11, 2013
  2. jcsd
  3. Feb 11, 2013 #2
    Yes, I think (a) is correct.
    Try drawing a principal-ray diagram to convince yourself.
     
  4. Feb 11, 2013 #3
    The magnification should be

    M = - Si/S
     
  5. Feb 11, 2013 #4
    Sorry, i believe i wrote that the wrong way round but i used M = -Si/S in my solution
     
  6. Feb 11, 2013 #5
    I've edited it now, but i still have the same problem in that the answer i have isn't the same as the answer provided
     
    Last edited: Feb 11, 2013
  7. Feb 11, 2013 #6
    Concave mirrors are used to shave or put on makeup since they produce virtual (Si negative and thus on the other side of the mirror) enlarged upright images as you found by a positive (upright image) larger than 1 (enlarged) magnification (image larger than object).
     
  8. Feb 11, 2013 #7
  9. Feb 13, 2013 #8
    Ok, turns out my answer was right. Thanks for your help everyone :)
     
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