A) \[{{45}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{90}^{o}}\]
D) \[{{180}^{o}}\]
Correct Answer: A
Solution :
The relation for restorative index of prism is given by \[\mu =\frac{\sin \,i}{\sin \,r}\] ?..(i) The condition for minimum deviation is given as \[r=\frac{A}{2}\] Here, prism angle \[A={{60}^{o}}\] Refractive index \[\times \mu =\sqrt{2}\] \[r=\frac{{{60}^{o}}}{2}={{30}^{o}}\] putting value of \[\mu \] and r in equation (i) we get, \[\sqrt{2}=\frac{\sin i}{\sin 30}\] \[\Rightarrow \] \[\sin \,i=\sqrt{2}\times \frac{1}{2}\] \[=\frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[\sin \,i=\sin {{45}^{o}}\] \[\Rightarrow \] \[i={{45}^{o}}\]
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