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Q.

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 $(S_{1})$ ?

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a

$\frac{λ}{(\sqrt{10} - 3)}$

b

$\sqrt{\frac{λ D}{2}}$

c

$\frac{λ}{2 (\sqrt{10} - 3)}$

d

$\frac{λ}{(10 - \sqrt{3})}$

answer is A.

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Detailed Solution

$x_{1} = 3 d, x_{2} = \sqrt{8} d$

For Ist min. $Δ x = \frac{λ}{2}$

$Δ x = x_{2} - x_{1} = \sqrt{8} d - 3 d = \frac{λ}{2}$

$\Rightarrow d = \frac{λ}{2 (\sqrt{8} - 3)}$

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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)?