| Consider a Young's double slit experiment as shown in figure. What should be the slit separation \[d\] in terms of wavelength \[\lambda \] such that the first minima occurs directly in front of the slit \[({{S}_{1}})?\] |
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A) \[\frac{\lambda }{2(\sqrt{5}-2)}\]
B) \[\frac{\lambda }{(\sqrt{5}-2)}\]
C) \[\frac{\lambda }{2(5-\sqrt{2})}\]
D) \[\frac{\lambda }{(5-\sqrt{2})}\]
Correct Answer: A
Solution :
\[\sqrt{{{(2d)}^{2}}+{{(d)}^{2}}}-2d=\frac{\lambda }{2}\] \[\Rightarrow \] \[(\sqrt{5}-2)d=\frac{\lambda }{2}\] \[\Rightarrow \] \[d=\frac{\lambda }{2(\sqrt{5}-2)}\]
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