Final answer:
The thickness of the thin film, given that the central maximum shifts by one fringe width in a double slit experiment, can be calculated using the formula λ/(2μ - 1), corresponding to option B: λ/(2μ - 1).
Step-by-step explanation:
The question involves determining the thickness t of a thin film introduced in front of one of the slits in a double slit experiment when the central maximum shifts by one fringe width. Using the principles of thin-film interference, we know that the path difference between the two rays should equal a multiple of the wavelength to produce constructive interference (a bright fringe). Since the central maximum shifts by one fringe width, this implies that the introduced path difference is one wavelength of the light used. The additional path difference introduced by the thin film is 2tμ because the light travels an extra 2t (forward and backward) within the film having a refractive index μ.
For the shift to be one wavelength λ of light, the path difference must thus be equal to the wavelength λ in the medium, which is λ/n where λ is the wavelength in vacuum and μ is the index of refraction.
Therefore, the thickness t can be found by setting 2tμ = λ, or t = λ/(2μ). However, if there is a phase change upon reflection, we need to consider half a wavelength more in the path difference, which adjusts the equation to 2tμ = λμ, leading us to the solution where t = λ/(2μ - 1). This corresponds to option B. λ/(2μ - 1).