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In my physics lab, we have to derive an equation. The equation is for a 45, 45, 90 degree triangle. An beam of light hits the surface, then refracts. The refracted beam hits the second surface at the critical angle and refracts along the surface. Here's a crude pic of what I'm talking about.

http://img379.imageshack.us/img379/615/pic13kt.jpg [Broken]

The equation is: √(2)*Sin (σ)+1=√(n^2-1)

The material is in air, so n1=1 and n2=n. So, Sin (σ1)=nSin(σ2). I moved around the upper equations and got Sin(σ)=[√(n^2-1)-1]/√(2)=nSin(σ2). This is where I'm having trouble. I'm not sure where to go from here. I know it has to do with Sin/Cos/Tan bits of the triangles that are made, but I can't figure it out. Any help will be appretiated. Thanks.

http://img379.imageshack.us/img379/615/pic13kt.jpg [Broken]

The equation is: √(2)*Sin (σ)+1=√(n^2-1)

The material is in air, so n1=1 and n2=n. So, Sin (σ1)=nSin(σ2). I moved around the upper equations and got Sin(σ)=[√(n^2-1)-1]/√(2)=nSin(σ2). This is where I'm having trouble. I'm not sure where to go from here. I know it has to do with Sin/Cos/Tan bits of the triangles that are made, but I can't figure it out. Any help will be appretiated. Thanks.

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