Obtain an expression of the displacement of the nth bright fringe in double slit experiment when a thin transparent plate of thickness t and refractive index  is introduced in the path of one of the two interfering waves. How the fringe-width is affected with the introduction of the plate?

When a thin transparent plate of thickness \( t \) and refractive index \( \mu \) is introduced into the path of one of the interfering waves in a double-slit experiment, the optical path length in that arm changes. This results in a phase difference between the two interfering waves, causing a shift in the position of the bright fringes.

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