A young's double slit experiment uses light of wavelength $900\; nm$ A plate of thickness 't' of material of refractive index $\mu=1.5$ i placed in front of one of the slits. What should be the thickness of plate 't' so that the central fringe becomes dark.

Question

$(a)\;4.5 \times 10^{-7}\;m \\ (b)\;9 \times 10^{-7}\;m \\ (c)\;1.5 \times 10^{-8}\; m \\ (d)\;4.5 \times 10^{-4}\;m $