A) \[2\,Co{{s}^{-1}}\frac{\mu }{2}\]
B) \[2\,Si{{n}^{-1}}\frac{\mu }{2}\]
C) \[2\,Co{{s}^{-1}}\mu \]
D) \[2\,Si{{n}^{-1}}\mu \]
Correct Answer: A
Solution :
Angle of incidence =2 (angle of refraction) i=2r Apply snell?s law \[\Rightarrow {{\mu }_{1}}\operatorname{Sin}\,i={{\mu }_{2}}Sin\,\operatorname{r}\] \[\Rightarrow 1\times \operatorname{Sin}\,2\operatorname{r}={{\mu }_{2}}Sin\,\operatorname{r}{{\mu }_{2}}=1(assum\,air)\] \[\Rightarrow \operatorname{r}=\frac{{{\cos }^{-1}}\mu }{2}\] \[\Rightarrow \operatorname{r}=\frac{i}{2}\] \[\operatorname{i}=2{{\cos }^{-1}}\frac{\mu }{2}\]
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