Question 102 of 191

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 $({S}_{1})$ ?

A$\dfrac{\lambda }{\left(5-\sqrt{2}\right)}$B$\dfrac{\lambda }{2\left(\sqrt{5}-2\right)}$C$\dfrac{\lambda }{2\left(5-\sqrt{2}\right)}$D$\dfrac{\lambda }{\sqrt{5}-2}$

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Answer: (C) $\dfrac{\lambda }{2\left(5-\sqrt{2}\right)}$

Path diff. in front of a slit on screen

$∆=\sqrt{5}d-2d=\left(2n-1\right)\dfrac{\lambda }{2}$

(for minima)

For ${1}^{st}$ minima $n=1$

$d\left(\sqrt{5}-2\right)=\dfrac{\lambda }{2}$

$d=\dfrac{\lambda }{2\left(\sqrt{5}-2\right)}$