A) \[{{\sin }^{-1}}\left( \frac{2}{3} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\]
D) \[ta{{n}^{-1}}\left( \frac{2}{3} \right)\]
Correct Answer: B
Solution :
For first diffraction minimum \[a\sin \theta =\lambda \] \[\Rightarrow \] \[a=\frac{\lambda }{\sin \theta }\] For first secondary maximum \[a\sin \theta =\frac{3\lambda }{2}\] or\[\sin \theta =\frac{3\lambda }{2}\times \frac{1}{a}=\frac{3\lambda }{2}\times \frac{\sin \theta }{\lambda }=\frac{3}{2}\times \sin {{30}^{o}}=\frac{3}{4}\] or\[\theta ={{\sin }^{-1}}\left( \frac{3}{4} \right)\]
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