# Calculating refraction in continuous refractive index

1. Jan 11, 2013

### vmedica

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. Jan 11, 2013

### haruspex

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.

3. Jan 11, 2013

### rude man

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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