Light Refraction on the Surface of a Sphere

[C. C.]

Hello All,
Using Snell's Law, it is pretty obvious how to calculate the angle of refraction when both index of refractions are known. My question is how would I apply this to a 3 dimensional situation, such as light refraction in a sphere? Since there are two angles in relation to the normal, how can I calculate the refraction? Any help would be greatly appreciated.

Thanks!

 

[nasu]

See this, for example. There are two "laws of refraction". Unfortunately too many times the first one is overlooked.

http://www.learnquebec.ca/en/content/curriculum/mst/opticks/chapter3/4_perception3.html

 

[C. C.]

Thanks for the link. You are absolutely correct that the first law is neglected when Snell's Law is taught. Since a new plane is formed from the surface normal and an incident ray, how would I go about tracing the refracted ray? Using Snell's Law, I can find the refracted ray on the new plane, but how can I track the refracted ray since it is on an arbitrary plane and can I find a relation to the origin? I guess the difficult part is trying to visualize this scenario. I hope that you can again point me in the right direction.

 

[A.T.]

how can I track the refracted ray since it is on an arbitrary plane and can I find a relation to the origin?

I think using vector math is the simplest way:
http://en.wikipedia.org/wiki/Snell's_law#Vector_form