A) \[\frac{4}{\pi }\sqrt{3}\times {{10}^{-2}}%\]
B) \[\frac{2}{\pi }\sqrt{3}\times {{10}^{-2}}%\]
C) \[\frac{1}{\pi }\sqrt{3}\times {{10}^{-2}}%\]
D) \[\frac{3}{\pi }\sqrt{3}\times {{10}^{-2}}%\]
Correct Answer: A
Solution :
[a] \[I={{I}_{0}}{{\sin }^{2}}\theta \Rightarrow \theta ={{\sin }^{-1}}\sqrt{\frac{I}{{{I}_{0}}}}\] \[d\theta =\frac{1}{2}\frac{\sqrt{{{I}_{0}}}}{\sqrt{{{I}_{0}}-I}}\frac{dI}{\sqrt{{{I}_{0}}\sqrt{I}}}\] \[\frac{d\theta }{\theta }=\frac{1}{2}\frac{dI}{\sqrt{I({{I}_{0}}-I)}\,{{\sin }^{-1}}\sqrt{I/{{I}_{0}}}}\] \[\therefore \,\,\,%\,error=\frac{4}{\pi }\sqrt{3}\times {{10}^{-2}}%\]
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