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 \[\theta =\frac{{{K}_{1}}{{\theta }_{1}}{{l}_{2}}+{{K}_{2}}{{\theta }_{2}}{{l}_{1}}}{{{K}_{1}}{{l}_{2}}+{{K}_{2}}{{l}_{1}}}\] \[\Rightarrow \] \[a=\frac{\lambda }{\sin \theta }\] For first secondary maximum 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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