A) \[si{{n}^{-1}}1\text{ (tan r }\!\!'\!\!\text{ )}\]
B) \[si{{n}^{-1}}1\text{ (tan r }\!\!'\!\!\text{ )}\]
C) \[{{\tan }^{-1}}1\text{ (Sin i }\!\!'\!\!\text{ )}\]
D) \[Co{{t}^{-1}}1\text{ (tan i }\!\!'\!\!\text{ )}\]
Correct Answer: B
Solution :
[b] \[\frac{1}{\mu }=\frac{\sin \,i}{Sin\,{{r}^{11}}}.....(1)\] \[r+{{r}^{1}}=90\] \[{{r}^{1}}=90-r\] \[sin\text{ }{{r}^{1}}=\text{ }\sin \,(90-r)=\text{ }cos\text{ }r\text{ }or\text{ }cos\text{ }i\] Put this value in (1) \[\frac{1}{\mu }=\frac{Sin\,i}{Cos\,r}=\frac{Sin\,i}{Cos\,i}=\tan \,i\] \[\sin \,{{i}_{c}}\,\tan \,i=\tan \,r\] \[{{i}_{c}}={{\sin }^{-1}}\,=[\tan \,r]\]
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