A Michelson Interferometer using a laser source of wavelength $\lambda_0 = 500\; nm$, with both the mirrors $(M_1$ & $M_2)$ fixed and positioned equidistant from the splitter/combiner is shown in the figure. When a dielectric plate of refractive index $n = 1.5$, of thickness $t$, is placed in front of the mirror $M_2$, a dark fringe is observed on the detector. When the dielectric plate is removed without changing the position of the mirrors $M_1$ & $M_2$, a bright fringe is observed on the detector. The minimum thickness $t$ (in $nm$) of the dielectric is ______________.
