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Problems with negatives.

  1. Sep 11, 2009 #1

    PrincePhoenix

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    1st problem:
    A small object of size 0.5 mm is placed close to a convex lens of focal length 5cm. The virtual image formed is at a distance of 25 cm from the lens. Find magnification.
    Data:
    focal length, f = 5cm
    distance of image , q = -25 cm (because image is virtual)
    distance of object , p = ?
    magnification, M = ?




    1/f = 1/p + 1/q
    M = height of image/height of object = q/p
    (ratio between height and distance of image and object)





    Solution:
    First finding p,
    1/f = 1/p + 1/q
    1/p = 1/f - 1/q
    1/p = 1/5 - (1/-25)
    ..................
    1/p = 6/25
    p = 25/6 = 4.16cm
    Now putting value of 'p' in magnification formula,
    M = height of image/height of object = q/p
    (ratio between height and distance of image and object)

    M = -25/4.16
    M = -6
    Can magnification be -ve? It is so in this problem. What have I done wrong?


    2nd problem:
    1-This part of a numerical problem as our teacher did it in classroom.
    Data:
    distance of object, p = 20cm
    focal length of concave lens,f = -19 (Is focal length of concave lens really always -ve?)
    distance of image, q = ?
    Solution:
    According to lens formula,
    1/f = 1/p + 1/q
    => 1/q = 1/f - 1/p
    1/q = 1/-19 - 1/20
    1/q = -20-19/380
    1/q = -39/380
    q = -9.74cm
    Why can't LCM be negative at line 4,5 of solution when one of the denominators is -ve? And is the -ve value of distance of image correct?
     
  2. jcsd
  3. Sep 11, 2009 #2

    Redbelly98

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    It should be -q/p in that equation.

    See previous note.
    By the way, magnification can be negative, and is when q and p are both positive.

    The LCM could be -380, but most people consider it easier to move the negative sign to the numerator and use a positive denominator.

    For a negative denominator, this becomes

    1/(-19) - 1/20
    = 20/(-380) + 19/(-380)
    = (+20 +19)/(-380)
    = ___?
     
  4. Sep 12, 2009 #3

    PrincePhoenix

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    Thanks.
     
  5. Sep 14, 2009 #4

    PrincePhoenix

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    What does negative magnification mean anyway?
     
  6. Sep 14, 2009 #5

    Redbelly98

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    It means the image is inverted, relative to the object. (Their heights have opposite signs.)
     
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