Calculating refraction in continuous refractive index

[vmedica]

Homework Statement

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

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.

Homework Equations

Snell's law?

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.

 

[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.

 

[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.