The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index is put in front of one of the slits, the central maximum gets shifted by a distance equal to n fringe widths. If the wavelength of light used is λ, t will be:

Concept:Young’s double-slit EXPERIMENT uses two coherent sources of light placed at a small distance apart, usually, only a few orders of magnitude greater than the wavelength of light is used.Calculation:Given,Thickness t and refractive INDEX μ,Shift = nβ (given)Path difference Δ = (μ - 1)tWhole pattern will be shifted by some amount given by,\(\therefore D\frac{{\left( {\MU - 1} \RIGHT)t}}{a} = \frac{{n\lambda D}}{a}\;\;\;\;\;\;\;\;\;\because \left[ {{\rm{Shift}} = \frac{{D\left( {\mu - 1} \right)t}}{a}} \right]\)The position of nth maxima and minima has shifted downward by the same distance which is called as\(S = \frac{{D\left( {\mu - 1} \right)t}}{a}\)Or\(\frac{{D\left( {\mu - 1} \right)t}}{a} = \frac{{n\lambda D}}{a}\)\(t = \frac{{n\lambda }}{{\mu - 1}}\)Therefore, t will be \(\frac{{n\lambda }}{{\mu - 1}}\)No option is matching. Therefore, this question should be awarded BONUS.