A) \[{{75}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{90}^{o}}\]
D) \[{{45}^{o}}\]
Correct Answer: B
Solution :
For a prism RI is given by \[\mu =\frac{\sin \left( \frac{A+\delta m}{2} \right)}{\sin \left( \frac{A}{2} \right)}\] ?..(i) Where, A = angle of prism Here, \[A={{60}^{o}},\mu =\sqrt{3}\] Putting the given value in equation (i), we get, \[\sqrt{3}=\frac{\sin \left( \frac{{{60}^{o}}+\delta m}{2} \right)}{\sin {{30}^{o}}}\] \[\sqrt{3}\times \sin {{30}^{o}}=\sin \left( \frac{{{60}^{o}}+\delta m}{2} \right)\] \[=\sin \left( \frac{{{60}^{o}}+\delta m}{2} \right)\] \[=\frac{\sqrt{3}}{2}=\sin {{60}^{o}}\] \[\Rightarrow \] \[\frac{{{60}^{o}}+\delta m}{2}={{60}^{o}}\] \[\Rightarrow \] \[{{60}^{o}}+\delta m={{120}^{o}}\] \[\Rightarrow \] \[\delta m={{120}^{o}}-{{60}^{o}}={{60}^{o}}\]
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