Đáp án:
n≈1,53
Giải thích các bước giải:
TA có:
\[\left\{ \begin{gathered}
A = {r_1} + {r_2} = 60^\circ \hfill \\
\sin 30 = n\sin {r_1} \hfill \\
n\sin {r_2} = \sin {i_2} = \sin 90 = 1 \hfill \\
\end{gathered} \right.\]
TA có:
\[\begin{gathered}
\cos \left( {{r_1} + {r_2}} \right) = \cos 60 = \frac{1}{2} \hfill \\
\Leftrightarrow \cos {r_1}\cos {r_2} - \operatorname{s} {\text{in}}{{\text{r}}_1}.\sin {{\text{r}}_2} = \frac{1}{2} \hfill \\
\Leftrightarrow \frac{{\sqrt {4{n^2} - 1} }}{{2n}}.\frac{{\sqrt {{n^2} - 1} }}{n} - \frac{1}{{2n}}.\frac{1}{n} = \frac{1}{2} \hfill \\
\Leftrightarrow \left( {4{n^2} - 1} \right)\left( {{n^2} - 1} \right) = {\left( {{n^2} + 1} \right)^2} \hfill \\
\Leftrightarrow 3{n^4} - 7{n^2} = 0 \hfill \\
\Leftrightarrow {n^2} = \frac{7}{3} \hfill \\
\Leftrightarrow n \approx 1,53 \hfill \\
\end{gathered} \]
