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Question: hi i am working on a physics problem but got...

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Hi, I am working on a physics problem but got stuck on the algebra part of the solution, can someone please help me with simultaneous equations?

I am applying Snell's Law to find the refractive index of a prism (n2), however, the only information I have is:

θ1=37°

θ4=90°

n1=1

And the two equations would be:

Eq. 1 - n1sinθ1=n2sinθ2   =>  1*sin(37)=n2sinθ2   =>  sin(37)=n2sin60-θ3   =>  n2=sin(37)sin60-θ3Eq. 2 - n2sinθ3=n1sinθ4   =>  n2sin(θ3)=1*sin90   =>  n2sin(θ3)=1   =>  n2=1sinθ3

This was an optics lab session and I am using a method called total internal reflection and then finding the refraction index from the critical angle (which is θ3 in this problem). After that point I used trig identities to resolve sin60-θ3 but then I got stuck and not sure if I equated the equations properly.

Thank you very much,

Michele

 

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