A) \[2{{\cos }^{-1}}\left( \frac{3}{4} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]
C) \[2{{\sin }^{-1}}\left( \frac{3}{2} \right)\]
D) \[{{\cot }^{-1}}\left( \frac{3}{2} \right)\]
Correct Answer: A
Solution :
Refractive index of prism \[\mu =\frac{\sin \frac{(A+{{\delta }_{m}})}{2}}{\sin \frac{A}{2}}\] \[=\frac{\sin (A+A/2)}{\sin (A/2)}=2\cos A/2\] or \[A=2\,{{\cos }^{-1}}\,\left( \frac{\mu }{2} \right)\] \[=2\,{{\cos }^{-1}}\,\left( \frac{1.5}{2} \right)=2\,{{\cos }^{-1}}\left( \frac{3}{4} \right)\]
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