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Simple Optics - being stupid?

  1. Feb 12, 2008 #1
    [SOLVED] Simple Optics - being stupid?!!!

    1. The problem statement, all variables and given/known data
    There's an object 1.5m from a white screen. What is the focal length of a lens needed to form a real and inverted image on the screen with magnification of 4.0?
    How far from the object should the lens be placed?


    2. Relevant equations
    -M=S'/S

    1/f=1/S'+1/S


    3. The attempt at a solution
    My problem is the first part of the question, what to use for S and S', surely there are an infinite number of possibilities?
     
  2. jcsd
  3. Feb 12, 2008 #2

    mgb_phys

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    You have a couple of extra constraints.
    1, the lens to image_distance is the focal length
    2, magnification = f / (f - object_distance)
    3, object_distance + image_distance = 1.5m
     
  4. Feb 12, 2008 #3
    I don't see how point 1 helps me sorry?

    I understand that objectdistance + imagedistance = 1.5m

    but that gives the distances sooo many possibilities?
     
  5. Feb 12, 2008 #4

    mgb_phys

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    image distance i = f, object distante = o
    i + o = 1.5m
    o = 1.5m - i = 1.5m -f

    m = f / ( f - o ) = 4

    subsitute o and solve for f
     
  6. Feb 12, 2008 #5
    right,

    if i follow that through i get f=8/3

    but then putting f back into m=f/(f-o) to find o,

    i get o=2, which cant be right because the object is only 1.5m from the screen?
     
  7. Feb 12, 2008 #6

    mgb_phys

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    Sorry my fault, image distance is only f if the object is at infinity (i'm an astronomer - objects are always at infinity!) I meant to say:
    1/f = 1/o + 1/i and o+i=1.5
    m = f / (f - o) = 4

    Rearrangement is a little trickier
     
  8. Feb 12, 2008 #7
    i'm really struggling with this... i cant seem to get f out of the maths?!
     
  9. Feb 12, 2008 #8

    kdv

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    maybe I am missing something here but S'/S = -M = 4 so S'= 4S, right? And S+S' = 1.5 meter so a simple substitution gives you both S and S'!!

    Then you may find the focal length using 1/f = 1/S + 1/S'. Iam probably missing something because it seems straightforward to me.
     
  10. Feb 12, 2008 #9
    You're right.... i feel like SUCH an idiot haha.

    Thanks!
     
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