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Thickness of lens and its focal length

  1. Mar 10, 2010 #1
    I'd like to ask
    does thinner convex lens give a shorter focal length?

    If so, why is it?

    thanks very much~~
     
  2. jcsd
  3. Mar 11, 2010 #2
    Hi there,

    The focal length of lens depends on curvature of the lens and the difference between the curved surfaces, as given by the lensmaker equation.

    [tex]\frac{1}{f} = (n-1)[\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{(n-1)d}{nR_{1}R_{2}}] [/tex]

    where

    f is the focal length of the lens,
    n is the refractive index of the lens material,
    R1 is the radius of curvature of the lens surface closest to the light source,
    R2 is the radius of curvature of the lens surface farthest from the light source, and
    d is the thickness of the lens between the curved surfaces

    If you reduce d then the focal length increases. If you mean making the lens less curved and hence thinner, then the curvature of the interfaces (R1 and R2) will increase and hence the focal length will increase.
     
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