Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength λ such that the first minima occurs directly in front of the slit (S1)?

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Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength λ such that the first minima occurs directly in front of the slit (S₁)?

$\frac{λ}{(5 - \sqrt{2})}$

$\frac{λ}{(\sqrt{5} - 2)}$

$\frac{λ}{2 (5 - \sqrt{2})}$

$\frac{λ}{2 (\sqrt{5} - 2)}$

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$\sqrt{{(2 d)}^{2} + {(d)}^{2}} - 2 d = \frac{λ}{2}$

$\Rightarrow (\sqrt{5} - 2) d = \frac{λ}{2}$

$\Rightarrow d = \frac{λ}{2 (\sqrt{5} - 2)}$