question_answer

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\[\left( {{S}_{1}} \right)\]? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) \[\frac{\lambda }{2(5-\sqrt{2})}\]            

B) \[\frac{\lambda }{2(\sqrt{5}-2)}\]

C) \[\frac{\lambda }{(5-\sqrt{2})}\] 

D) \[\frac{\lambda }{(\sqrt{5}-2)}\]

Correct Answer: B

Solution :

At point \[P\,\Delta x=\sqrt{5}d\,\,-\,\,2\,d\] \[\Delta \,x=d\left( \sqrt{5}-2 \right)\] For first minima \[\Delta \,x\,\,=\,\,\frac{\lambda }{2}\] \[d=\,\frac{\lambda }{2(\sqrt{5}-2)}\]