A) \[26{}^\circ \]
B) \[0{}^\circ \]
C) \[23{}^\circ \]
D) \[13{}^\circ \]
Correct Answer: D
Solution :
Given: Angle of the prism \[=30{}^\circ \] Refractive index \[\mu =\sqrt{2}\] The relation for refractive index is given by \[\mu =\frac{\frac{A+{{\delta }_{m}}}{2}}{\sin \frac{A}{2}}=\frac{\sin \frac{{{30}^{o}}+{{\delta }_{m}}}{2}}{\sin \frac{\sin {{30}^{o}}}{2}}\] \[\sqrt{2}=\frac{\sin \frac{{{30}^{o}}+{{\delta }_{m}}}{2}}{\sin 150}\] or \[\sin =\frac{{{30}^{o}}+{{\delta }_{m}}}{2}=\sqrt{2}\sin {{15}^{o}}\] or \[\sin =\frac{{{30}^{o}}+{{\delta }_{m}}}{2}=1.414\times 0.2588\] or \[\sin =\frac{{{30}^{o}}+{{\delta }_{m}}}{2}=0.3659\times =0.366\] or \[\frac{{{30}^{o}}+{{\delta }_{m}}}{2}={{\sin }^{-1}}0.366={{21.46}^{o}}={{21.5}^{o}}\] or \[{{30}^{o}}+{{\delta }_{m}}={{43}^{o}}\] \[{{\delta }_{m}}={{43}^{o}}-{{30}^{o}}={{13}^{o}}\]
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