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3. hi i am working on a physics problem but got...

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

###### Question details

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:

${\theta }_{1}=37°$

${\theta }_{4}=90°$

${n}_{1}=1$

And the two equations would be:

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