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Derive a final formula from two other formulas

  1. Apr 27, 2010 #1
    Using these two formulas derive the third formula:

    D/l = (D+f)/(l+alpha)
    D/r = (D+f)/(r+beta)

    D=(fb)/(alpha+beta)

    where D is the distance of the point from the line between the viewer's eyes;
    f is the focal length of the lens in the eye; b is the distance between the two eyes;
    and the sum of the terms α and β is referred to as the disparity.




    Is this right?
    1. D/l=(D+f)/(l+alpha) --> flip --> l/D=(l+alpha)/(D+f)
    2. D/r=(D+f)/(r+beta) --> flip --> r/D=(r+beta)/(D+f)

    Add 1 and 2
    (l+r)/D=((l+alpha)+(r+beta))/(D+f)

    l+r=b

    b/D=(b+alpha+beta)/(D+f)

    cross multiply

    b(D+f)=D(b+alpha+beta)
    bD+bf=Db + Dalpha + Dbeta
    bf = Db+Dalpha+Dbeta-bD
    bf=Dalpha + Dbeta
    bf = D(alpha+beta)

    D = bf/(alpha+beta)
     
    Last edited: Apr 27, 2010
  2. jcsd
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