A) \[\theta >{{\cos }^{-1}}\left[ \mu \sin \left( A+{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
B) \[\theta <{{\cos }^{-1}}\left[ \mu \sin \left( A+{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
C) \[\theta >{{\sin }^{-1}}\left[ \mu \sin \left( A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
D) \[\theta <{{\sin }^{-1}}\left[ \mu \sin \left( A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
Correct Answer: C
Solution :
By snell?s law at 1st refracting surface is \[1.\sin \theta =\mu .\sin {{r}_{1}}\] \[\sin {{r}_{1}}=\frac{\sin \theta }{\mu }\] \[{{r}_{1}}<{{\theta }_{1}},\] ray to transmitted through surface AC, \[{{r}_{2}}<{{\theta }_{c}}\]\[{{r}_{2}}<{{\sin }^{-1}}\left( \frac{1}{\mu } \right)\] \[A-{{r}_{1}}<{{\sin }^{-1}}\left( \frac{1}{\mu } \right)\] \[A-{{\sin }^{-1}}\left( \frac{\sin \theta }{\mu } \right)<{{\sin }^{-1}}\left( \frac{1}{\mu } \right)\] \[A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right)<{{\sin }^{-1}}\left( \frac{\sin \theta }{\mu } \right)\] \[\sin \left( A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right)<\frac{\sin \theta }{\mu }\] \[\mu \sin \left( A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right)<\sin \theta \] \[\theta >{{\sin }^{-1}}\left( \mu \sin \left( A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right)\]You need to login to perform this action.
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