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