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Homework Help: Refraction/Smallest curve of optical fibre.

  1. Sep 26, 2007 #1
    1. The problem statement, all variables and given/known data

    "figure 3" (below) shows an optical fibre bent in a curve. The diameter of the fibre is 4mm. If light is not to escape, calculate the smallest radius of R of the curve round which the fibre can be bent. Assume that the fibre is surrounded by air (refractive index 1) and that the refractive index of glass is 1.5"

    Phys-1.jpg


    2. Relevant equations

    n1
    ___ = SinC (critical angle)

    n2

    3. The attempt at a solution

    Well, Ive got c, the critical angle -

    1
    __ = 0.666.... sin-1(o.666) = 41.81
    1.5

    But, I can seem to make a triangle with enough information to get R. I've tried splitting it up, but either get not enough information to do sine or cosine rules, or a non right angle triangle. Maybe I'm just missing something?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 26, 2007 #2

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    Call the acute angle at the centre between the dashed and dotted lines A.
    If the fibre makes a quadrant then the angle between the incoming ray and the dotted line is 90 therefore angle A is 90-C.
    The dotted line is length R, the hypotonuse (dashed line) is R+4mm and the angle is (90-c)
    So cos(90-C) = r/(r+4mm)
     
  4. Sep 26, 2007 #3
    So just rearrange that to give me R? Ill give it a shot.
     
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