MU }_{1}}\,\sin {{\theta }_{1}}={{\mu }_{2}}\,\sin {{\theta }_{2}}\] \[\cos {{\theta }_{1}}=\frac{10}{\SQRT{{{(6\sqrt{3})}^{2}}+{{(8\sqrt{3})}^{2}}+100}}\] \[=\frac{10}{\sqrt{400}}=\frac{10}{20}\] \[\Rightarrow \] \[{{\theta }_{1}}={{60}^{o}}\] \[\sqrt{2}\,\sin {{60}^{o}}\,=\sqrt{3}\,\sin {{\theta }_{2}}\] \[\Rightarrow \] \[\sqrt{2}\times \frac{\sqrt{3}}{2}=\sqrt{3}\sin {{\theta }_{2}}\] \[\Rightarrow \] \[\sin {{\theta }_{2}}=\frac{1}{\sqrt{2}}\,\Rightarrow \,\,\,{{\theta }_{2}}={{45}^{o}}\]

"> 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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Let the \[x-y\] plane be the boundary between two transparent media. Medium 1 in \[z\ge 0\] has refractive index of \[\sqrt{2}\] and medium 2 with \[z<0\] has a refractive index of \[\sqrt{3}\]. A ray of light in medium 1 given by the vector \[\vec{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\,\hat{j}-10\hat{k}\] is incident on the plane of separation. The angle of refraction in medium 2 is

Joint Entrance Exam - Main (JEE Main) Physics in Joint Entrance Exam - Main (JEE Main) . 10 months ago

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[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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Posted on 08 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Physics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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