A) \[0{}^\circ \]
B) \[30{}^\circ \]
C) \[45{}^\circ \]
D) \[60{}^\circ \]
Correct Answer: C
Solution :
The refractive index of prism \[{{\mu }_{1}}=\sqrt{2}\] The refractive index of medium \[{{\mu }_{2}}=2\] The relation between critical angle and refractive index is given by \[{{\mu }_{2}}=\frac{1}{\sin C}\Rightarrow \sin C=\frac{1}{{{\mu }_{2}}}=\frac{1}{2}=\sin {{30}^{0}}\] \[\Rightarrow \] \[C={{30}^{o}}\] As given that, angle of prism is equal to critical angle. Hence, \[C=A={{30}^{o}}\] So, angle of reflection \[r={{30}^{o}}\] \[\mu =\frac{\sin i}{\sin r}or\sqrt{2}=\frac{\sin i}{\sin {{30}^{o}}}\] So, \[\sin i=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}=\sin {{45}^{o}}\] Angle of incidence\[i={{45}^{o}}\]
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