Angle of an emerging ray through two boundaries

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SUMMARY

The discussion focuses on calculating the angle of an emerging ray of light as it passes through two parallel boundaries, specifically from air into diamond and back into air. The key principle applied is Snell's Law of refraction, which must be utilized twice to determine the angles at each boundary. The angle of incidence at the second boundary is directly related to the angle of refraction at the first boundary, denoted as θ2. This method provides a systematic approach to solving problems involving multiple boundaries in optics.

PREREQUISITES
  • Understanding of Snell's Law of refraction
  • Basic knowledge of light behavior at boundaries
  • Familiarity with angles of incidence and refraction
  • Ability to interpret optical diagrams
NEXT STEPS
  • Study the application of Snell's Law in multi-boundary scenarios
  • Explore the concept of critical angles and total internal reflection
  • Learn about the refractive indices of different materials, including diamond
  • Investigate advanced optics topics, such as ray tracing techniques
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Students and professionals in physics, optics engineers, and anyone interested in understanding light behavior at material boundaries.

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Thank-you for taking the time to read my problem. I am currently doing work with light and boundaries and have come across a question that I am having a hard time understanding. I know how to calculate angles when they go through one boundary but I can not figure out how to do it when there is 2 boundaries.

Look at the diagram. Calculate the angle of the emerging ray in air. Assume that the first and second boundaries are parallel.
Diagram: http://img27.imageshack.us/img27/6221/scan.jpg
(thanks to http://www.imageshack.us/ for the free image hosting)

I understand the question well. The ray is in air, crosses the boundary into the diamond, and then crosses the second boundary back into air where I have to figure out the angle. Where I am stumped is that second boundary. Thank-you for any help you may be able to give me.
 
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Snell's law-done twice

Apply Snell's law of refraction at each boundary. Question/hint: if the angle of refraction of the light after crossing the first boundary is [itex]\theta_2[/itex], what will be the angle of incidence of that light before crossing the second boundary?
 
Thank-you very much for your help. It was able to give me a good start into the question. :).
 

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