In the ideal YDSE , when a glass plate $(refractive index\;1.5)$ of thickness t is introduced in path of one of interfering beams (wave - length $\lambda$) the intensity at position where central maximum occurred preciously remains unchanged . The minimum thickness of glass plate is :

Question

$(a)\;2 \;\lambda \\ (b)\;\frac{\lambda}{3} \\ (c)\;\frac{2 \lambda}{3} \\ (d)\;\lambda$