A Michelson Interferometer using a laser source of wavelength 𝜆0 = 500 nm

Q. A Michelson Interferometer using a laser source of wavelength 𝜆₀ = 500 nm, with both the mirrors (𝑀₁& 𝑀₂) 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 𝑀₂ , a dark fringe is observed on the detector. When the dielectric plate is removed without changing the position of the mirrors 𝑀₁& 𝑀₂, a bright fringe is observed on the detector. The minimum thickness 𝒕 (in nm) of the dielectric is     

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Ans: 250