# 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 (${n}_{2}$), however, the only information I have is:

${\theta}_{1}=37\xb0$

${\theta}_{4}=90\xb0$

${n}_{1}=1$

And the two equations would be:

$Eq.1-{n}_{1}\mathrm{sin}\left({\theta}_{1}\right)={n}_{2}\mathrm{sin}\left({\theta}_{2}\right)=1*\mathrm{sin}\left(37\right)={n}_{2}\mathrm{sin}\left({\theta}_{2}\right)=\mathrm{sin}\left(37\right)={n}_{2}\mathrm{sin}\left(60-{\theta}_{3}\right)={n}_{2}=\frac{\mathrm{sin}\left(37\right)}{\mathrm{sin}\left(60-{\theta}_{3}\right)}$$Eq.2-{n}_{2}\mathrm{sin}\left({\theta}_{3}\right)={n}_{1}\mathrm{sin}\left({\theta}_{4}\right)={n}_{2}\mathrm{sin}\left({\theta}_{3}\right)=1*\mathrm{sin}\left(90\right)={n}_{2}\mathrm{sin}\left({\theta}_{3}\right)=1={n}_{2}=\frac{1}{\mathrm{sin}\left({\theta}_{3}\right)}$

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 ${\theta}_{3}$ in this problem). After that point I used trig identities to resolve $\mathrm{sin}\left(60-{\theta}_{3}\right)$ but then I got stuck and not sure if I equated the equations properly.

Thank you very much,

Michele