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 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 :

[b]

At point \[P\,\Delta x=\sqrt{5}d\,\,-\,\,2\,d\]

\[\Delta \,x=d\left( \sqrt{5}-2 \right)\]

For first minima \[\Delta \,x\,\,=\,\,\frac{\lambda }{2}\]

\[d=\,\frac{\lambda }{2(\sqrt{5}-2)}\]