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Power of a spherical refracting surface

  1. Jun 8, 2006 #1
    The power of a spherical refracting surface is given as, P = (n2 – n1)/R
    Where n1 = refractive index of object space, n2 = refractive index of image space
    R = Radius of curvature of the spherical surface
    I tried to derive the expression but I got a different expression.
    Let u and v be the object and image distance from the spherical surface respectively.
    Suppose the spherical refracting surface produces the image of a real object placed at its first principal focus at infinity. Then,
    u = +f1, v = infinity
    For refraction at a spherical surface,
    (n2)/v + (n1)/u = (n2 – n1)/R
    (n2)/(infinity) + (n1)/f1 = (n2 – n1)/R
    0 + (n1)/f1 = (n2 – n1)/R
    f1 = [(n1)(R)]/( (n2 – n1)
    Power = 1/f1
    Therefore P = (n2 – n1)/[(n1)(R)]
    Could you please tell me where I have gone wrong?
  2. jcsd
  3. Jun 8, 2006 #2

    Andrew Mason

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    It looks like f1 is the focal length in air (n = 1). The power is the reciprocal of the focal length in the medium. That focal length is f1/n1 in a medium with index of refraction n1. So the power is P = n1/f1

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