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Homework Help: Thin Lenses Focal Length

  1. Feb 8, 2010 #1
    Let's say that there are three lenses A (all of which are semicircles: flat on one side, curved on the other). One lense is a short and curved D, another lense is a very elongated and narrow D (longer than the first lense), and the third lense is as long as the second lense but has a sharper curvature. How would you rank the focal lengths of these lenses? In other words, how is focal length of a lense related to its shape? More curved = shorter focal length? Longer lens = longer focal length?
     
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  3. Feb 8, 2010 #2

    mgb_phys

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    The more steeply curved the shorter the focal length = the greater the bending effect on the light. A completely flat piece of glass has an infinite focal length and no bending effect
     
  4. Feb 8, 2010 #3
    I have a similar question, i knew about the curvature, but how does the SIZE of the lens affect the focal length? do smaller (shorter) lenses have shorter focal points than longer lenses?
     
  5. Feb 8, 2010 #4

    mgb_phys

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    No - only the curvature affects the focal length
     
  6. Feb 8, 2010 #5
    Thanks! So, lets continue with the D-shaped lenses, if you have a short lense and a tall lense, and the width of the lenses (from the center of flat edge to the center of the curved edge) are equal, the short lens would have a smaller focal length since its relative curvature is higher than the longer lense, which doesnt have as steep of a curve (despite having equal width)?
     
  7. Feb 9, 2010 #6

    mgb_phys

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    The focal length of a lens is set by the 'lens maker equation'
    1/f = n(1/r1 - 1/r2)

    D shaped (we call them plano-convex) only depend on the curvature of of one side since the other side is flat (ie r=infinite and 1/r=0)

    The thickness of the lens doesn't matter (as far as focal length is concerned)

    The diameter of the lens does matter for the amount of light the lens can receive (important in the first element of binoculars or a telescope) or for the range of angles it can receive light from (important in the elements at the back of a camera lens)

    ps. Technically we call an individual 'lens' (ie one bit of glass) an element. A system of several elements working together - like in your camera is called a 'lens'.But when you only have a single element - like in a magnifying glass - this is also called a lens.
    There is no such word 'lense' people think this because in english the plural is lenses
     
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