In a double-slit experiment light of wavelength 632nm produces a central bright fringe on the screen. A thin transparent plate of refractive index μ=1.50 is now introduced in the path of one of the interfering beams.
(a) Derive an expression for the additional optical path difference introduced by a plate of thickness t placed in the path of one beam.
(b) Calculate the minimum non-zero thickness tmin of the plate that will shift the central bright fringe to the position originally occupied by the first dark fringe.
(c) State, with justification, whether the central point on the screen after insertion of this plate will appear bright or dark when the calculated thickness tmin is used.