Light Refraction on the Surface of a Sphere

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Discussion Overview

The discussion centers around the application of Snell's Law to light refraction on the surface of a sphere, exploring how to calculate the angle of refraction in a three-dimensional context. Participants are particularly interested in the complexities introduced by the spherical geometry and the implications for tracing refracted rays.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions how to apply Snell's Law to a three-dimensional situation involving a sphere, noting the challenge of calculating refraction with two angles relative to the normal.
  • Another participant references the existence of two "laws of refraction," suggesting that the first law is often overlooked in discussions of Snell's Law.
  • A participant expresses the need for guidance on tracing the refracted ray on an arbitrary plane formed by the surface normal and the incident ray, indicating difficulty in visualizing the scenario.
  • One suggestion is made that vector math may provide a simpler approach to tracking the refracted ray in this context.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best method to calculate and visualize the refraction of light on a spherical surface, and multiple viewpoints on the application of Snell's Law and vector math are presented.

Contextual Notes

The discussion highlights the complexity of applying Snell's Law in three dimensions, particularly regarding the formation of new planes and the visualization of refracted rays, which may depend on specific definitions and assumptions not fully articulated in the thread.

C. C.
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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!
 
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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
 
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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.
 

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