A) \[\tan {{\,}^{-1}}(\sin \,i)\]
B) \[\tan {{\,}^{-1}}(\sin \,i)\]
C) \[{{\sin }^{-1}}\,{{(\tan \,i)}^{-1}}\]
D) \[\sin {{\,}^{-1}}(\tan \,r)\]
Correct Answer: C
Solution :
It is quite clear \[r+r=90{}^\circ \] or \[r=90{}^\circ -r\] and \[i=r\] The refractive index is given by \[\mu =\frac{\sin i}{\sin r}=\frac{\sin i}{\sin \,(90{}^\circ -r)}=\frac{\sin i}{\cos r}\] \[=\frac{\sin i}{\cos i}=\tan i\] Now \[\frac{1}{\sin C}=\tan i\] \[\Rightarrow \] \[\sin C={{(\tan i)}^{-1}}\] so, \[C={{\sin }^{-1}}{{(\tan i)}^{-1}}\]You need to login to perform this action.
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