A) \[2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
B) \[{{\sin }^{-1}}\left( \mu \right)\]
C) \[{{\sin }^{-1}}\left( \frac{\mu }{2} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
Correct Answer: A
Solution :
The refractive index\[(\mu )\]of a material is the factor by which the phase velocity of electromagnetic radiation is slowed down in that material. From Snells law \[\mu =\frac{\sin i}{\sin r}\] Given, \[i=2r\] \[\therefore \] \[\mu =\frac{\sin 2r}{\sin r}\] Using \[\sin 2\theta =2\sin \theta \cos \theta \] \[\therefore \] \[\mu =\frac{2\sin r\cos r}{\sin r}=2\cos r\] \[\Rightarrow \] \[r={{\cos }^{-1}}\left( \frac{\mu }{2} \right)\] Hence, angle of incidence is \[i=2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]You need to login to perform this action.
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