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[Lens] given: focal length and magnification, find image distance and image height

  1. Dec 8, 2011 #1
    1. The problem statement, all variables and given/known data

    With a lens with f = 25 cm, we want to project an image that is 5 times bigger than object, so M = 5

    - Find the image distance s'
    - Find the image height Hi

    2. Relevant equations

    1/f = 1/s + 1/s'

    M = s'/s = Hi/Ho

    With:
    f = focus distance of lens
    M = magnification
    s' = image distance
    s = object distance
    Hi = image height
    Ho = object height

    3. The attempt at a solution

    From the second equation we get: 1/s = M/s'

    Substitute that in first equation to get s':

    1/f = M/s' + 1/s' --> s' = (M+1)f = (5+1)*25 = 150 cm

    The problem is now i don't know how to get the image height...from our answer we can easily calculate that s = 30 cm, so we know:

    M = 5
    f = 25 cm
    s = 30 cm
    s' = 150 cm

    how do i get Hi?
     
  2. jcsd
  3. Dec 8, 2011 #2
    Re: [Lens] given: focal length and magnification, find image distance and image heigh

    You're missing the formula that related object and image distances to object and image heights
     
  4. Dec 8, 2011 #3
    Re: [Lens] given: focal length and magnification, find image distance and image heigh

    That is the second formula M = s'/s = Hi/Ho...but i only have s' and s, and i have to determine Hi
     
  5. Dec 8, 2011 #4
    Re: [Lens] given: focal length and magnification, find image distance and image heigh

    I think I'm brain dead. Can't you find one of the heights using the same technique you used finding the object and image distances?
    You have M = Hi/Ho and you have s and s'
    in terms of Hi and Ho to use in your focal length equation so you can make two equations I think. Try it.
     
    Last edited: Dec 8, 2011
  6. Dec 8, 2011 #5
    Re: [Lens] given: focal length and magnification, find image distance and image heigh

    I don't think this excersise can be done...however i flip or turn it i always end up with M= Hi/Ho = 5....but with x/y = 5 we have two variables and one equation. I think the teacher made a mistake when he gave this excersise out.
     
  7. Dec 8, 2011 #6
    Re: [Lens] given: focal length and magnification, find image distance and image heigh

    I'll run it again in the morning. I did solve it but I could have made a mistake.
     
  8. Dec 8, 2011 #7

    ehild

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    Homework Helper
    Gold Member

    Re: [Lens] given: focal length and magnification, find image distance and image heigh

    The object height is not given. You can say only that the image height is 5 times the object height.

    ehild
     
  9. Dec 9, 2011 #8
    Re: [Lens] given: focal length and magnification, find image distance and image heigh

    Intuitively it didn't seem possible but I ran it a couple of times and didn't get anywhere either. If you draw a ray diagram using the given information I can't see that the information give in any way restricts the height of object and image other than one being 5 times larger than the other.
     
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