A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{75}^{o}}\]
Correct Answer: B
Solution :
[b] \[{{\mu }_{1}}\,\sin {{\theta }_{1}}={{\mu }_{2}}\,\sin {{\theta }_{2}}\] |
\[\cos {{\theta }_{1}}=\frac{10}{\sqrt{{{(6\sqrt{3})}^{2}}+{{(8\sqrt{3})}^{2}}+100}}\] |
\[=\frac{10}{\sqrt{400}}=\frac{10}{20}\] |
\[\Rightarrow \] \[{{\theta }_{1}}={{60}^{o}}\] |
\[\sqrt{2}\,\sin {{60}^{o}}\,=\sqrt{3}\,\sin {{\theta }_{2}}\] |
\[\Rightarrow \] \[\sqrt{2}\times \frac{\sqrt{3}}{2}=\sqrt{3}\sin {{\theta }_{2}}\] |
\[\Rightarrow \] \[\sin {{\theta }_{2}}=\frac{1}{\sqrt{2}}\,\Rightarrow \,\,\,{{\theta }_{2}}={{45}^{o}}\] |
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