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 \( \left(S_{1}\right) \) ? [JEE Main-2019 (January)] (a) \( \frac{\lambda}{2(\sqrt{5}-2)} \) (b) \( \frac{\lambda}{(\sqrt{5}-2)} \) (c) \( \frac{\lambda}{2(5-\sqrt{2})} \) (d) \( \frac{\lambda}{(5-\sqrt{2})} \)

Question

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 \( \left(S_{1}\right) \) ? [JEE Main-2019 (January)] (a) \( \frac{\lambda}{2(\sqrt{5}-2)} \) (b) \( \frac{\lambda}{(\sqrt{5}-2)} \) (c) \( \frac{\lambda}{2(5-\sqrt{2})} \) (d) \( \frac{\lambda}{(5-\sqrt{2})} \)

Comments

In second solution
 deta x = root 5d  -2d