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Homework Help: Calculating refraction in continuous refractive index

  1. Jan 11, 2013 #1
    1. The problem statement, all variables and given/known data

    The problem is page 5 on: http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/Paper3_2010_.pdf [Broken]

    I will just summarise the question:

    The refractive index of space,n, at a distance r from the sun is given by √(1+5920/r). The light from a distant star is deflected by a small angle θ. Using a simple model, calculate θ.

    2. Relevant equations

    Snell's law?

    3. The attempt at a solution

    I have no idea of how to get started with this question. I think that the model will involve some discrete layers but I still wouldn't know how to do the problem. Any help would really be appreciated.
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 11, 2013 #2


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    Yes, use Snell's law. Consider a ray of light that would pass some distance s from the sun passing through a thin annulus at radius r. You can calculate the angle at which it intersects that annulus and hence the small adjustment to its trajectory. I think you can treat s as unchanging, since the deflection is small.
  4. Jan 11, 2013 #3

    rude man

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    Seems to me data is missing, especially how close to the sun's surface does the beam get. I suppose you could make your answer a function of that distance as another poster suggests.

    Then I'd say you need to do an integration of an infinite number of infinitely thin layers with n a function of r. For each layer Snell's law would apply.
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