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