In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56 , the central fringe shifts to the position of 7^ th bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thickness of mica sheet is 10⁻⁹ m. The value of is ______.

Step-by-step solution

The shift in the central fringe due to the introduction of a transparent sheet of thickness t and refractive index is given by y = D d ( - 1)t . The position of the n^ th bright fringe is y_n = n D d . Equating the two, we get: D d ( - 1)t = n D d ( - 1)t = n Substituting the given values: (1.56 - 1)t = 7 450 10⁻⁹ 0.56 t = 3150 10⁻⁹ t = 3150 0.56 10⁻⁹ t = 5625 10⁻⁹ m Comparing with t = 10⁻⁹ m, we get = 5625 . Answer: 5625