A plate of thickness x made of refractive index $\mu $ is placed in front of one of the slits in a double slit experiment. What should be minimum thickness x . so that the central maxima turns to fringe with minimum intensity

Question

$(a)\;(\mu -1) \frac{\lambda}{2} \\ (b)\;(\mu-1) \lambda \\ (c)\;\frac{\lambda}{2 (\mu-1)} \\ (d)\;\frac{\lambda}{\mu-1} $