Question

Consider a young's doluble slit experiment as shown in figure. What should be the slit seperation d in term of wavelength $\lambda$ such that the first minima occurs directly in front of the slit $\left(S_1\right)$ ?

• A. $\frac{\lambda }{2(5-\sqrt{2})}$
• B. $\frac{\lambda }{(5-\sqrt{2})}$
• C. $\frac{\lambda }{(\sqrt{5}-2)}$
• D. $\frac{\lambda }{2(\sqrt{5}-2)}$

Answer 1

Answer: (D)

$\frac{\lambda }{2(\sqrt{5}-2)}$

$x_1=2d$

$x_2=\sqrt{5}d$

$\Delta x=x_2-x_1$

$\sqrt{5}d-2d=\frac{\lambda }{2}$

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