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Homework Help: Thin lens equation with multiple lenses

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Heres the problem exactly as written:

    A system of lenses is composed of three lenses. Calculate the maximum magnification these three lenses will achieve if the lenses are located 35.0 cm apart. The lenses have focal lengths of 15.0, 20.0, and 25.0 cm.

    2. Relevant equations
    1/p + 1/q = 1/f
    M = q/p = h`/h

    3. The attempt at a solution
    I am confused on the maximum magnification part. It seems that would depend on where you placed the object or would it matter in which order the lenses are placed? An hints would be greatly appreciated.
  2. jcsd
  3. Jan 18, 2009 #2
    The object would be outside the lens system and the virtual image would be viewed on the other side of the lense system. Switching the image position and the object would lead to the same answer due to symmetry. The problem is finding the arrangement of the three lenses such that a maximum magnification occurs. I'm assuming these are convex thin lenses thus forming a compound microscope. With this assumption the final magnification is the product of the linear magnification (which you showed) and the angular magnification which is

    m angular = θ'/θ

    where θ is approximately equal to h/near point of eye where near point of the eye is 25 cm and θ' = h/f so,

    m angular = 25 cm/f

    For a two lens compound mircoscope, the first image must be real in order to form the object for the second lens. Extend this to the three lens system. Then by brute force rearrange the configuration to evaluate the magnification for each case.
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