A) \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{2}{3} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]
Correct Answer: D
Solution :
For the first minima, \[\theta =\frac{\eta \lambda }{a}\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,\sin 30{}^\circ =\frac{\lambda }{a}=\frac{1}{2}\] First secondary maxima will be at, \[\sin \theta =\frac{3\lambda }{2a}=\frac{3}{2}\left( \frac{1}{2} \right)\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\theta ={{\sin }^{-1}}\left( \frac{3}{4} \right)\]
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