Derive the expression Sinc =n2/n1
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the easiest way is to start with n_1\sin \theta _i = n_2\sin \theta _r . Note that at a critical angle of incidence, the angle of refraction is 90 degrees and you know that the sine of 90 degrees is 1.
\implies n_1 \sin \theta _c = n_2
\implies \sin \theta _c = \frac{n_2}{n_1} , where n_1 is the optically denser medium
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