A) \[45{}^\circ C\]
B) \[60{}^\circ C\]
C) \[90{}^\circ C\]
D) \[180{}^\circ C\]
Correct Answer: A
Solution :
The relation for refractive index of prism is \[\mu =\frac{\sin i}{\sin r}\] ...(i) The condition for minimum deviation is \[r=\frac{A}{2}=\frac{{{60}^{o}}}{2}={{30}^{o}}\] Putting the given values of\[\mu =\sqrt{2}\]and\[r=30{}^\circ \]in eq (i), we get \[\sqrt{2}=\frac{\sin i}{\sin {{30}^{o}}}\] or \[\sin i=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}\] \[\sin i=\sin {{45}^{o}}\] \[\therefore \] \[i={{45}^{o}}\]
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