[tex]\text{Salut,pornind de la legea Snell-Descartes:}\\
n_1\cdot\sin i=n_2\cdot \sin r(\text{unde }n_1=1\text{ ,iar }n_2=n)\\
\text{Prin urmare legea se scrie:}\\
\sin i=n\cdot \sin r\\
\text{Facem un artificiu de calcul:}\\
\sin i=n\cdot tg\ r\cdot \cos r\\
\sin i=n\cdot tg\ r\cdot \sqrt{1-\sin^2 r}\\
tg\ r=\dfrac{\sin i}{n\sqrt{1-\sin^2 r}} \\
\text{Dar stim ca } \sin r=\dfrac{\sin i}{n}\\
\text{Inlocuim in relatia de mai sus si obtinem:}[/tex][tex]tg\ r=\dfrac{\sin i}{n\sqrt{1-\frac{\sin^2 i}{n^2}}}=\dfrac{\sin
i}{n\cdot \frac{1}{n}\sqrt{n^2-\sin^2 i}}}=\boxed{\dfrac{\sin
i}{\sqrt{n^2-\sin^2 i}}}[/tex]
