On replacing a thin film of mica of thickness $12 \times 10^{-5}$ cm in the path of one of the interfering beams in Young's double slit experiment using monochromatic light, the fringe pattern shifts through a distance equal to the width of bright fringe. If $\lambda = 6 \times 10^{-5}$ cm, the refractive index of mica is
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When the shift is equal to $n$ fringe widths, the optical path difference introduced is $(\mu - 1)t = n\lambda$.