Question
In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$ , the path difference (in terms of an integer $n$) corresponding to any point having half the peak intensity is :-
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Answer
${{\rm{I}}_{\pi {\rm{et}}}} = {{\rm{I}}_0} + {{\rm{I}}_0} + 2{{\rm{I}}_0}\cos \phi = \frac{{{{\rm{I}}_{\pi ax}}}}{2} = 2{{\rm{I}}_0}$
$\Rightarrow \cos \phi=0 \Rightarrow \phi=n \pi+\frac{\pi}{2}=\frac{2 \pi}{\lambda} \Delta x$
$\Rightarrow \Delta x=(2 n+1) \frac{\lambda}{4}$
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