A) \[75{}^\circ \]
B) \[60{}^\circ \]
C) \[45{}^\circ \]
D) \[30{}^\circ \]
Correct Answer: D
Solution :
Applying the formula for refractive index \[(\mu )\] of a prism having angle of prism A \[\mu =\frac{\sin \frac{A+\delta m}{2}}{\sin \frac{A}{2}}\] ?(1) Putting the given values of\[\mu =\sqrt{2}\] and angle of prism \[\text{A = 6}{{\text{0}}^{\text{o}}}\] in the Eq. (1), we get \[\sqrt{2}=\frac{\sin \frac{{{60}^{o}}+\delta m}{2}}{\sin \frac{{{60}^{o}}}{2}}=\frac{\sin \frac{{{60}^{o}}+\delta m}{2}}{\sin {{30}^{o}}}\] or \[\sin \left( \frac{{{60}^{o}}+\delta m}{2} \right)=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}\] or \[\sin \frac{{{60}^{o}}+\delta m}{2}=\sin {{45}^{o}}\] or \[{{60}^{o}}+\delta m={{90}^{o}}\]or \[{{\delta }_{m}}={{90}^{o}}-{{60}^{o}}={{30}^{o}}\]
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