A) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
B) \[{{\sin }^{-1}}\left( \sqrt{\frac{9}{8}} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{5}{7} \right)\]
Correct Answer: C
Solution :
The angle of incidence in denser medium for which the angle of refraction in rarer medium is \[{{90}^{o}}\] is called the critical angle [C]. \[{{\mu }_{w}}\] and \[{{\mu }_{g}}\] are refractive indices for rarer (water) and denser (glass) media, then \[\frac{\sin C}{\sin {{90}^{o}}}=\frac{{{\mu }_{w}}}{{{\mu }_{g}}}\] \[\Rightarrow \] \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\] \[\Rightarrow \] \[C={{\sin }^{-1}}\left( \frac{8}{9} \right)\] Note: The critical angle for water-air, glass-air and diamond-air interfaces are \[{{49}^{o}},{{42}^{o}}\] and\[{{24}^{o}}\] respectively.You need to login to perform this action.
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