A) \[2{{\cos }^{-1}}(3/4)\]
B) \[{{\sin }^{-1}}(3/4)\]
C) \[2{{\sin }^{-1}}(3/2)\]
D) \[{{\cos }^{-1}}(3/2)\]
Correct Answer: A
Solution :
According to question, the angle of minimum deviation \[{{\delta }_{m}}=\]Refracting angle Refractive index, \[\mu =\frac{\sin \left( \frac{A+{{\delta }_{m}}}{2} \right)}{\sin \left( \frac{A}{2} \right)}\] \[=\frac{\sin \left( \frac{A+A}{2} \right)}{\sin \left( \frac{A}{2} \right)}\] \[=\frac{\sin A}{\sin \left( \frac{A}{2} \right)}\] \[=\frac{2\sin \left( \frac{A}{2} \right).\cos \left( \frac{A}{2} \right)}{\sin \left( \frac{A}{2} \right)}\] \[\frac{3}{2}=2\cos \left( \frac{A}{2} \right)\] \[\cos \left( \frac{A}{2} \right)=\frac{3}{4}\] \[\frac{A}{2}={{\cos }^{-1}}\left( \frac{3}{4} \right)\] \[A=2{{\cos }^{-1}}\left( \frac{3}{4} \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
